i giggled furiously at the 80085 on the calculator. your videos are always worth the time to watch, great job
@rasszo8729
Жыл бұрын
I thought there would be more ppl commenting on that.
@nicco1690
Жыл бұрын
Then does that mean that the 8085 microprocessor is BOBS?
@wtmayhew
Жыл бұрын
@@rasszo8729 It is easier to see on a seven segment display. Gotta be old school!
@JS-bf9dw
Жыл бұрын
Me too xDDDDD That was a great detail
@wisteela
Жыл бұрын
I didn't notice that.
@Otto1871
Жыл бұрын
It feels like Dave has worked on everything
@anntallexgamer4630
Жыл бұрын
What didn't he work on?
@bubbavonbraun
Жыл бұрын
Windows 11 🙂
@ProtekNickz
Жыл бұрын
maybe that's why it feels terrible
@davidrush4908
Жыл бұрын
@@ProtekNickzThe basic code base is the essentially the same. Fix some bugs, add some more. Make everything look a little different to make people believe it's new.
@BillAnt
Жыл бұрын
Flat Earthers (aka Flatheads) still think it equals 1. lol
@ramosel
Жыл бұрын
I'm so glad I sent you that Mach 10 board... it's so nice to see it actually running again after sitting in a box for 20+ years. I still have the TI SR-52 I went off to the Naval Academy with.
@billj5645
Жыл бұрын
There were somewhat similar products on the market from other companies. I remember I went into SoftWarehouse to buy one and they told me they had stopped selling their particular model "because it was a crappy product".
@rotten-Z
Жыл бұрын
Wiki:In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[1] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[26] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.
@laurencefraser
Жыл бұрын
And if they're specifying it's because they're not following the standard convention that everyone would assume they were using if they didn't. And if they're doing something non-standard Without specifying, then they are doing their readers/students a major disservice.
@rotten-Z
Жыл бұрын
@@laurencefraser It says that standards and agreements are different. PEMDAS is not absolute
@OriginalNuckChorris
Жыл бұрын
PEMDAS is for little kids... and Americans.
@myrryr1
Жыл бұрын
They are specifying it because some people are from the US, and need it explicitly spelled out for them@@laurencefraser
@AEVMU
4 ай бұрын
And if they are simply clarifying, or simply doing it that way without comment, you can't conclude anything. @@laurencefraser
@BobHutton
Жыл бұрын
When I did maths at uni many years ago, we hardly ever used the divide by (÷) symbol. It was long enough ago that everything was hand written. Instead we would draw a long horizontal line, with all the other bits either above or below the line. The convention then was you first evaluated the bits above and below the line separately, then performed the division. I'm guessing part of the problem has been in moving to on-screen text, some have assumed the ÷ symbol did the same job, with everything on the left assumed to be above the line and everything on the right assumed to be below the line.
@maxrburgess
Жыл бұрын
I *always* put that stuff in a bunch of sets of parentheses.
@lufax
Жыл бұрын
Yes, that's the right way to do it. PEMDAS or BODAS or whatever is just a short hand for (English-speaking) school kids that ends up doing more harm than good. The actual rule is "don't be ambiguous". And that's why you test calculators to check how they process ambiguous situations. They are neither right or wrong if they show 1 or 9. They just interpret in different ways
@brostenen
Жыл бұрын
Those two and a third are what we learn here in Denmark. We learn how to write it in three different ways in primaery school, and told to use what we personally find the easiest to use. And nobody learn PEMDAS. It is way too complicated. We learn reduction. Meaning 6÷2(2+1) becomes 3x3. Way more simple.
@markm1514
Жыл бұрын
THIS
@ANDELE3025
Жыл бұрын
Not a problem. Real issue is dave never learned math past grade school and is adding a operation that doesnt exist in between the number of a unknown unit and the unit itself. Aka he doesnt know how to solve 6:2n where n=3 and instead writes himself some unrelated problem of 6/2*3
@oisiaa
Жыл бұрын
Dave....you going through Windows 1, 2, 3.1 were a pure nostalgia trip for me. I'm only 36, but 3.1 was the first OS I used. It's pure emotion to see these old operating systems in use!
@ahabsbane
Жыл бұрын
So you were like 4?
@oisiaa
Жыл бұрын
@@ahabsbane It would have been between Windows 3.1's release and Windows 95, probably closer to 6 or 7.
@ahabsbane
Жыл бұрын
@@oisiaa I figured, I'm not much older than you, just having a laugh at our age. I remember installing the "turbo" upgrade chip for the 386 with my Gramps. If I'm being honest he's probably the reason I'm in the field I am today. He was always trying out the newest tech before the rest of the family, computers, GPS, cell phones, he was quite the techie old man!✌️
@gashnal
Жыл бұрын
honestly same, i will be 40 soon thats why i fallow Dave, the man coded a large part of my childhood.
@subtledemisefox
Жыл бұрын
I'm the same age and the same first OS. Or would it be DOS? I mean the two were kind of inseparable lol
@velzekt4598
Жыл бұрын
Actually Dave, the Windows 1.0 calculator was entirely correct. It looks like you hit add instead of multiply, so you entered 6/2+1 which does in fact come out to 4 :) (you can rewatch the footage and you'll see that the + was pressed but * never was)
@carloscases96
Жыл бұрын
You are right
@adamg8588
Жыл бұрын
What's the time
@rh4009
Жыл бұрын
Clearly Dave should've typed at 75%, then his answer might've been 100%
@toolbaggers
Жыл бұрын
He should rewatch it at 75% speed 😎
@rh4009
Жыл бұрын
@@toolbaggersFor some reason, adding the word "speed" makes the joke less funny.
@nickryan3417
Жыл бұрын
Formula such as 6/2x(2+1) are exactly why when writing code, or elsewhere, I always included brackets to make the calculation order very clear. It solved a lot of potential issues when the not-so mathematically literate came across them and made them easier to tweak later too. On the other hand, I once programmed in a computer language where the statement "a = a + 1" produced a different result to "a = 1 + a". That took some effort to get to the bottom of why, someone else's code, just was not working as expected. If the starting value of a was 10, the first completed with a having a value of 11. However, the second statement left a completed with the value of 2.
@emlynmatheson4589
Жыл бұрын
What language was that? That's a super interesting thing - was it some sort of weird typecasting issue?
@DavesGarage
Жыл бұрын
When I write code, I use a lot of parenthesis to make both math and casts clear!
@RDCST
Жыл бұрын
What? 1+10 != 10+1?
@Phryj
Жыл бұрын
It looks like it is treating the + operator as an "increment by 1" function that doesn't accept any parameters after the operator.
@Vibe77Guy
Жыл бұрын
@@DavesGarage I used to write in LISP... (Lost In Stupid Parentheses) For AutoCad applications.
@joweraDE
Жыл бұрын
Great video, but counterargument: Multiplication by juxtaposition or implied multiplication may be interpreted as having higher precedence as division. So your old calculator is also right (as well as my expensive Casio calculator I bought a year ago) The real takeaway is: Just use parentheses
@kevinyonan9666
Жыл бұрын
I say get rid of the quotient symbol and only use fractions, even for kids grade math
@0LoneTech
Жыл бұрын
This, as shown by the Sharp calculator, is the traditional version, known as PEJMDAS in response to the misdescription of PEMDAS. The background is documented in some detail in a video titled "The Problem with PEMDAS: Why Calculators Disagree" on the channel "The How and Why of Mathematics". The short of it is, some American teachers (whose experience came from recent and incomplete textbooks, not reading applied maths) decided to claim their unusual interpretation was "the correct way", and convinced Casio to release some calculators with their version, causing severe confusion ever since. Most textbooks espousing that strict PEMDAS without regard for juxtaposition don't even follow it themselves.
@papa_smerf7603
Жыл бұрын
It's called PEJMDAS and is the only way in science and nearly everythink outside USA.
@maticjelovcan
Жыл бұрын
@joweraDE, yes and also knowing what's the purpose of the calculation, because (6/2)(3*1) will be different than 6/(2(3*1)). The math is not a problem, but what do you want to do with it and how do you express it.
@dduncane
Жыл бұрын
yup, but in the end, as said by some other it's more the way the math problem is written that is the problem, it's ambiguous ...
@8_Bit
Жыл бұрын
The ambiguity is due to reducing a "chalk board" style problem that involves fractions (with numerator / denominator) down to a single line. The "slash" symbol could indicate that the question is 6 over 2(2+1), in which case the answer is 1. Or it could be interpreted as 6 divided by 2, times (2+1), answer 9. The question is deliberately imprecise.
@JonathanGray89
Жыл бұрын
It's not about the slash symbol. Some people intuitively treat multiplication by juxtaposition as having a higher precedence. Some people even claim that's how they were taught.
@xnamkcor
Жыл бұрын
6 over all would be (6)/(all).
@jamesdurtka2709
Жыл бұрын
@JonathanGray89 if it were 2x instead of 2(1+2) then that is absolutely how most people do juxtaposed multiplication. 2x always means double x, no matter what comes before or after!
@cassiee.3969
Жыл бұрын
@@JonathanGray89 > Some people even claim that's how they were taught. Because we were. Incidentally, it's also how mathematicians publishing mathematical papers in mathematical journals CONSISTENTLY interpret the order of operations.
@JonathanGray89
Жыл бұрын
@@cassiee.3969 I hate that KZitem automatically censors my comments and I can only find out with in-cognito mode. I have to rewrite them and paraphrase just to get my point across. Anyway, you're not only wrong, but you're also dishonest. I can link a video right now of an actual mathematician saying the answer is 9. The fact of the matter is mathematicians are overwhelmingly aware of this ambiguity and simply avoid it. At the very least that's what some mathematicians are claiming. Don't make assumptions about how mathematicians interpret the order of operations just because you already think you're right.
@bastian_5975
Жыл бұрын
Pemdas was invented by someone to explain it as easily as possible, but nobody used it in reality. There's an extra step: multiplication by juxtaposition, which takes precedence over explicit multiplication and division. If you look in math text books, you will see that something like √12 will often be simplified down to 2√3, and then if you do math with that, say 2÷2√3, it will come out as 1/√3. By your logic, we should be getting just √3. The true order of operations is PEJMDAS. It was just stickler teachers who insisted that what the book says in text (without looking at what the actual math evaluates out to) is right 100% of the time that pushed pemdas. Pemdas is inconsistently followed. If you go back to google and type in 2/2pi, you will se they follow pejmdas and convert it to 2/(2*pi). Ultimately the most important rule is to be consistent. Pejmdas is what most people actually use before "corrections" to pemdas, and pejmdas still sneaks through in cases like 2pi.
@Boffin55
Жыл бұрын
likewise, the reactance of a capacitor is 1 / 2πfc; where all of the implied multiplication happens prior to division.
@robincal1
Жыл бұрын
Yeah I remember this formula. So if teachers followed PEMDAS, they should have also written this as 1/2/π/f/c?@@Boffin55
@cassiee.3969
Жыл бұрын
Exactly. And it was the same stickler teachers who would think they were clever when they tried to correct our use of contractions by saying "ain't ain't a word because ain't ain't in the dictionary" without considering that they might should check the dictionary before making a claim like that. They did *not* think it was funny when you then went and found ain't in the dictionary and then you showed them in front of the entire classroom. Which is extra funny, because that sort of teacher usually at least claimed to be Christian. You know, that religion that says pride is a sin? I guess I know where Ms. Paguaga is going to be spending eternity 🙄
@cericat
Жыл бұрын
@@cassiee.3969 she'll be in good company with my Mormon stepfather, he had the same attitude about ain't but pride is far from his only sin.
@kktech04
Ай бұрын
Wrong ! There can't be two scalar products with different precedence rules. That would lead to absurd results.
@barrellcooper6490
4 ай бұрын
The problem with things like this is: you write the equation, so don't write ambiguous equations. Write the expression the way that reflects what you want to happen.
@durragas4671
3 ай бұрын
This right here. Math on its own as just numbers doesn't mean much. If you know the units you are solving, the numbers are just a quantity - and you know what you want operations you want to perform on them.
@skeith452
Жыл бұрын
The calculator isn't necessarily wrong. It just uses a slightly different version of PEMDAS. The 2 multiplying the parenthesis is treated as what can be called an "implied multiplication" (because it has no multiplication symbol) which is supposed to be resolved before other multiplication and divisions. Part of why I prefer to abuse parenthesis to avoid this kind of funky stuff.
@mattgaia
Жыл бұрын
Correct. The reason that people get 1 for an answer is 2(2+1) would be using implicit multiplication (or multiplication by juxtaposition) which has a higher precedence than multiplication/division.
@ANDELE3025
Жыл бұрын
@@mattgaia Which in turn is based on basic axioms of sets and substitution which anyone, especially dave, should know. You can substitute any part of the equation with unknown element (6:2n, n:6, 6:2(n+1), 6:2(2+n) and any way you can resolve the problem without outright just doing something you arent allowed to results in 1. Brackets and operation symbols exist for a reason.
@terben7339
Жыл бұрын
I think that Dave is just magicking away the parentheses in this example. Ask yourself, does 2(2+1) = (4+2)? If it does, then what is the solution to 6÷(4+2)?
@wwusirius
Жыл бұрын
Yeah it's not wrong, both are valid. Almost every academic paper that I've seen will utilize implied multiplication as higher precedence. 1/2x for example resolves to 1/(2x). How many times I've seen stuff like pV/RT = n in school, or 1/2pi. It's obvious that they are linked. Just because the calculators shown are being forced into evaluating it strictly by a convention developed by educational institutions doesn't mean that the academic world uses it.
@Vithigar
Жыл бұрын
@@wwusirius How many academic papers are you reading that use inline division? Showing division unambiguously above or below the dividing bar is overwhelmingly the preferred presentation.
@henrikjensen3278
Жыл бұрын
Try using: 6/2A You say it is: (6/2)*A But in formulas it is usually accepted as 6/(2A) Or do you say a () is handled different from a letter? In my HP Prime calculator it is not a issue. It do not use RPN, but shows divide as true horizontal line with factors above and below.
@Poldovico
Жыл бұрын
If you're using variables with inline division, you're basically a criminal. But then you'd have to stick with the rules: your monomial there is 3a, not 3a^-1
@evgen5647
Жыл бұрын
Yep, some people will still say it's (6/2)*A, declining any other opinion. May I ask where are you from, which country?
@henrikjensen3278
Жыл бұрын
@@evgen5647 From Denmark, Europe. I have seen this problem before, it has basically existed as long as calculators with implied multiplication. In books 3/2A is usually taken as 3/(2*A), but this is not much of an issue anymore because modern typesetting can use a true horizontal line. Today some people want a strict PEMDAS rule, other accept a modified rule where implied multiplication take precedent.
@evgen5647
Жыл бұрын
@@henrikjensen3278yep, Europe. You see, USA are freakingly fanatic about PEMDAS because they were tought this way. India as well I believe (which is a bit strange taking into account that India was British colony for some time).
@alexmack851
Жыл бұрын
@@evgen5647even in American they don't use PEMDAS in scientific papers. Google the America Physical Society style guide. on page 21 it shows research papers should have multiplication before division
@stevenspencer306
Жыл бұрын
I argue that the answer is indeed 1. The ambiguity of the equation comes from the use of one line division in conjunction with the use of implicit multiplication. Implicit multiplication just feels like it has an implied grouping to it as well. i.e. 2(2+1) should always be expanded to (2*(2+1)) when used in a larger expression rather than simply 2*(2+1). Another way to think about it is n(x) is the n-times function. i.e. n(x){return n*x}. Would you still try to tell me that 6/n(x) should return (6/n)*x instead of 6/(n*x)?
@AntiHeadshot
Жыл бұрын
So true. But "garbage in, garbage out", is the reason.
@pretol2730
Жыл бұрын
most people would have little problem recognizing implied over explicit priority in examples like "5 ÷ 2n"...
@okaro6595
Жыл бұрын
No, professional mathematicians and physicians constantly use implied multiplication in in-line expressions and it has a higher precedence. Who are you to tell professionals they do it wrong because of what your elementary school teacher said?
@herrbonk3635
Жыл бұрын
6/2(1+2)=1. An implied multiplication *always* goes before any explicit operator. 1/2π = 1/(2π), for instance. That's the standard in mathematics, science and engineering since centuries back.
@Boffin55
Жыл бұрын
Agreed. A simple google of "Multiplication by Juxtaposition" will find thousands of references explaining that implied multiplication is treated as the same precedence as brackets
@forkless
11 ай бұрын
The problem is that that is up to interpretation due to the "standard" used. Even PEMDAS is being interpreted differently depending on the calculator you use.
@herrbonk3635
11 ай бұрын
@@forkless How? The syntactical conventions has been settled since the 1800s... just look at older scientific texts! I studied mathematics and science in the 1980s and 90s. Never heard of "pemdas", "pejmdas" or similar... until KZitem... The fact that some calculators give the wrong result must be due to these strange american attempts to change the standard. Perhaps sloppy programming in some cases.
@ricomariani
Жыл бұрын
1. It can mean whatever you want it to mean it's just notation and notation is not math 2. They teach PEMDAS and such to children so people think it's axiomatic or something, it's nothing of the sort. 3. In advanced math, probably the most common convention, and it's only that, is that adjacency is higher than infix. Hence 1/3x is not (1/3)x but rather 1/(3x). === from wikipedia (and this jives with my experience) Mixed division and multiplication In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[1] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[21] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[b] This ambiguity is often exploited in internet memes such as "8÷2(2+2)", for which there are two conflicting interpretations: 8÷[2(2+2)] = 1 and [8÷2](2+2) = 16.[22] The expression "6÷2(1+2)" also gained notoriety in the exact same manner, with the two interpretations resulting in the answers 1 and 9.[23] Ambiguity can also be caused by the use of the slash symbol, '/', for division. The Physical Review submission instructions suggest to avoid expressions of the form a/b/c; ambiguity can be avoided by instead writing (a/b)/c or a/(b/c).[21] [24] === It turns out to be very convenient that ab/cd is not the same as abd/c But a wise person will just avoid this stuff. The only "real" answer is that it's ambiguous. The proof of which is that people, even clever people, disagree. Even those that wrote calculators. But it wouldn't be hard for me to find a page in one of my calculus books that shows the more common way to interpret this after grade school is to boost adjacency. Still it is whatever you want it to be. It's not axiomatic as some people like to say. None of the axioms deal with notation. RPN would work just as well. Another way to avoid this problem is to never use infix division but always make fractions. But that doesn't work so well for writing single lines of text. Anyway, it's whatever.
@ricomariani
Жыл бұрын
I guess another interesting thought is this. The purpose of order of operations is to make it so that you can write more expressions with less parens. Hence multiplication goes first because that's more convenient and for no other reason. Adjacency being stronger than infix is also more convenient because it gives you a few more ways to avoid parens. But none of this is law and indeed even advanced math publications do not universally agree.
@TomNimitz
4 ай бұрын
Exactly. PEMDAS works for elementary school math before algebra and more advanced formula notations are taught, but falls short in real world applied mathematics where juxtaposition and many other mathematical notations are just not covered by PEMDAS. (We also learn about seven colors in the rainbow and the Bohr model of the atom - oversimplifications that we later learn to set aside. )
@olzk4705
4 ай бұрын
Exactly this. I recall having a bunch of lessons in school class of Algebra where we were exercising in interpretation of division notations. The solution is straight-forward: default to Landau-Lifshitz-Feynman, and if the expression in the video has to be interpreted to yield 9 not 1, simply rewrite it, move the part in parentheses to the dividend, to avoid misinterpretation. In this (Landau-Lifshitz-Feynman notation) case, reading one-liners like ab/cd is unambiguous
@RaspK
4 ай бұрын
@@ricomariani There is another reason why adjacency is generally treated as stronger: consistency. In mathematical notation, we often use expressions such as e.g. "2x² + 3y + z" or some such; so, either nx is supposed to be treated the same as (n*x) at all times, or it is inconsistent. Therefore, mathematicians (rather than math afficionados) tend to prefer this analytical approach. Still, the reality is that it's deemed as ambiguous and therefore preferably avoided altogether (the way e.g. linguists avoid using archaic words which are typically misused by the general public, unlike journalists who insist on butchering them).
@dman375
6 күн бұрын
adjacency is higher than infix ONLY applies with equations, NOT expressions... becasue that 3 is the COEFFICIENT of x... There is no such thing with expressions... 1/3 * 3 = 1 1/3x where x = 3 = (1/9) And YES... notation absolutely matters becasue it communicates expectations... which is kind of important in math!
@jamesdurtka2709
Жыл бұрын
The discourse around this often forgets that these notational conventions are fairly arbitrary and don't always agree. For instance, if we replace (1+2) with x most people would probably agree that 6/2x is best read as 6/(2x) and not (6/2)x. At least, that's the closest approximation to what one normally writes on paper with pencil - which typically bypasses the ambiguity altogether. Regardless, this notational ambiguity means that PEMDAS is better understood as a rule of thumb, not a prescriptive formula for the correct way to do arithmetic written in a computer-friendly notation.
@evgen5647
Жыл бұрын
Yep, some people will still say it's (6/2)*x, declining any other opinion. May I ask where are you from, which country?
@JonathanGray89
Жыл бұрын
There is no problem with the order of operations. The expression is ambiguous. The mathematical term is "not well defined". The problem is with the expression.
@Poldovico
Жыл бұрын
On paper, though, how often do you use inline division? If you're not using fraction lines, chances are you're already deviating from paper habits.
@JonathanGray89
Жыл бұрын
For the record I was explicitly taught that multiplication by juxtaposition should be treated as regular multiplication. I definitely question the logic of how anyone could think 6/2x would be any different from 6/2(x).
@evgen5647
Жыл бұрын
@@JonathanGray89 your math teacher was dumb-ass and tried to tought you the incorrect logic. The only correct logic nowadays is that this expression is unambigious and avoid unambiguity in exact sciences at all costs.
@EyMannMachHin
Жыл бұрын
I'm not entirely sure, but in my mind the implict multiplication (the one where you can leave out "x"..) binds stonger than any operand. So my mind will make 6/(2*(1+2)) out of it. Simply because I'm used to working with formulas and have been taught to keep the variables in until the expression has been simplified as much as possible, before adding any number into it. And I'm used to doing that on paper so I always know what the dividend and what the divisor is.
@MrSas1972
Жыл бұрын
Totally agree, 2(1+2) is not the same as 2*(1+2) the first notation means give me content of parenthesis twice the second regular PEMDAS multiplication
@ksarnelli
Жыл бұрын
What's you're talking about is called PEJMDAS and it's a real thing (J for juxtaposition). Some modern calculators do use PEJMDAS and many allow you to switch between PEMDAS and PEJMDAS, so there is really no "right" answer here - it just depends on which order of operations you're using.
@cirion66
Жыл бұрын
Meanwhile I put anything ambiguous into parentheses, so there is no room for an error. Most code language linters will force you to do so anyway, because consistency is important.
@hectorg.7282
Жыл бұрын
@@ksarnelliYou don't have to add the J. This works with PEMDAS. The parenthesis takes precedence and cannot be eliminated the way he did in the video. He performed the addition inside the parenthesis and eliminated it without first performing the implied operation of the parenthesis, you cannot do that. Why did he not do this years ago? Well, because back then he would have not gotten any traction from all the idiots in the Internet.
@MichaelCoates
Жыл бұрын
You're describing the distributive property a(b+c) = ab + AC Solving left to right as described in the video would break this law of mathematics
@davedaley9093
Жыл бұрын
Evaluate 1÷2π. Does it equal 1.5708 or 0.1592? In a textbook formula it would be 1/2π. I was taught (in the '50's) that multiplication by juxtaposition took precedence over explicit operators. This included x(value) without an intervening operator.
@lenonkitchens7727
3 ай бұрын
Here's my problem with Dave's video and explanation, and PEMDAS in general. Using PEMDAS, and Dave's rules and logic: 1 / 2(pi) = 0.1592 but... 1 / 2(1 + 2.14) = 1.5708 therefore... 1 / 2(3.14) = 1.5708 The answer can't change because you replace a variable with literal numbers. That's the whole point of a variable. It represents a literal number that you may or may not know. Using PEJMDAS, the answer to all of the above is 0.1592, which is the correct answer if you were to use that equation in the real world. Therefore PEMDAS is wrong, or at least incomplete, and therefore Dave is wrong on this one.
@CallousCoder
2 ай бұрын
@@lenonkitchens7727absolutely Dave and the boys at Microsoft are wrong in this case, because of juxtaposition! It really is PEJMDAS but the statement is ofcourse purposely ambiguous. But an engineer and mathematician will see the indirect multiplication result and (correctly) execute those first.
@steinanderson9849
Ай бұрын
@@CallousCoder a mathematician will evaluate based upon the notation standard used - whether it is pemdas or pejmdas. pemdas and pejmdas are not rules of evaluating equations, they are in fact rules of notation.
@CallousCoder
Ай бұрын
@@steinanderson9849 that’s true, and therein lies the problem. It’s ambiguous. But juxtaposition comes before division. I can’t link to a great video by a lady who explains the history of pemdas. And juxtaposition and that’s how we’ve been taught. And than the answer is 1. Also because the obulus says that what comes to the right goes on the top dot and what goes to the left goes on the bottom dot. So 1 -- 2pi And thus you do juxtaposition before you do the division. Otherwise you would write (1 ➗ 2)pi SHARP calculators always just PEJMDAS and Casio change because daft American teachers who did pemdas. But now they went back to the PEJMDAS (like the rest of the world) Look for the video with the title: The Problem with PEMDAS: Why Calculators Disagree And you see why Dave (original poster) and I stand firm that implied multiplication comes before division.
@steinanderson9849
Ай бұрын
@@CallousCoder stand firm all you want. at the end of the day the standard of notation is what prevails and depending on your environment implicit multiplication being of higher priority may or may not be the standard. simple stuff really.
@RenderingUser
Жыл бұрын
for me, the answer is 1 not because thats the "correct" answer there isnt one its because that's the answer according to the writing convensions id use id interpret 6 / 2(2+1) as a/bc and id consider bc to be one single whole complete product i make a distinction between ab and a * b
@SilverSpade92
Жыл бұрын
Most of the modern calculators assume "bc" are seperate products, which is probably for the best, cuz how else would you clarify that? You can simply use another pair of brackets to make the calculators read them as one product: 6 / 2(2+1) = 9 6 / (2(2+1)) = 1 Try it out =)
@RenderingUser
Жыл бұрын
@@SilverSpade92 adding brackets suck I prefer writing as efficiently as possible It's just easier to keep ab as one product by default and make a * b an operation than it is to have ab default to a * b and having to add 2 brackets to two sides to determine the values are together. So I'll stick with the old calculators.
@chad_bro_chill
Жыл бұрын
@@SilverSpade92 No way, that first expression should have parenthesis around the fraction, especially given that it's going to be multiplied by something after it. You shouldn't have more numerator after the denominator unless it's clearly marked. (6/2)*(2+1) is the only correct way to write that first expression, that or reordering it to (6*(2+1))/2.
@johanlarsson9805
Жыл бұрын
@@chad_bro_chill You start by doing a misstake and then the rest is wrong. since there is no operator writen out it is 6/(2(2+1)) You are simply showing that you have not done enough math to grasp it.
@DairyAir
Жыл бұрын
Dude, I love your random stuff… I have ADHD really bad, which makes reading nearly impossible… People like you, doing things like this, is sooo helpful… Adult education is key to building our world… Educated people can be very intimidating… it’s a special talent, to bridge that…
@Acetyl53
Жыл бұрын
No, you don't "have ADHD really bad". You have something that's screwing your brain up which you need to be solving, instead of taking on a meme diagnosis as an identity.
@DairyAir
Жыл бұрын
@@Acetyl53 you mean well… Do you wanna learn about what you have wrong? It’s more than “getting distracted”… I don’t think “in words”… for me to “read,” I have to “visualize” it… I can do it. It just takes forever. Now, live in a world, where everyone else reads something, and then waits for you, to take 3 times longer, to read… That stress causes a “fight or flight” response, in people… When I’m trying to read, my subconscious is looking for excuses to avoid continuing reading… After a while, you naturally avoid those situations.
@Acetyl53
Жыл бұрын
@@DairyAir I understand this, however you have to realize I more than mean well, I'm right. You have to run around in this labyrinth of compensation because your brain is being disrupted. Get off whatever drugs they have you on in whatever course is encessary, get on a multivitamin, and try cutting out rgains for a while. Look for evidence of mold in your environment. Lastly avoid wireless devices. You can do it. Don't accept the FALSE soothing of submitting to the disabed identity.
@wilfridtaylor
6 ай бұрын
@@DairyAir Sounds more like dyslexia than ADHD but go get a proper diagnosis from a professional. Can help a lot.
@herehere3139
5 ай бұрын
@@DairyAirAbsolutely, Tons and tons of people dont "believe" in mental illness etc, typically because they cant "see" it. If they saw a broken leg, Yeah they would believe it was broken. But they cant see the difference in pathways that certain brains take or lack of etc And they also wont spend the time to understand. So they just stay stupid and arrogant. Thats ok though.i have been diagnosed add and bipolar type 2, my brain is very different and im a natural with music and music production, therefore its what i have always done. It just makes sense to me. I wish i could program, and i have dabbled a good bit, But holy hell its a mouthful of learning. It needs to be practiced like trying to be advanced on an instrument. Blah blah blah ✌️
@vitajazz
Жыл бұрын
"I'd cut him some slack, because (A) He'd be a 108 years old, and (B) he passed away a long time ago." Logical as always. I Loved this episode, which for me does clarify using brackets in equations. Unfortunately my old Sharpe scientific calculator no longer works, nor does my original TI with plasma display.
@DavesGarage
Жыл бұрын
Ooooh! I love plasma displays.
@mwaringmlw
Жыл бұрын
My Sharpe always uses parentheses.
@John-McAfee
Жыл бұрын
@@DavesGarageThere is not a universally recognized convention for evaluating this expression. It is technically ambiguous as to what the answer is in the video. 6/2(2 + 1) = 6/[2(2 + 1)] = 1 is juxtaposed [and implicit]. 6/2 (2 + 1) = (6/2) (2 + 1) = 9 is implicit but not juxtaposed. 6/2 × (2 + 1) = (6/2) (2 + 1) = 9 is explicit multiplication. These questions are always written to be ambiguous to make people have long and pointless arguments about it.
@X22GJP
Жыл бұрын
@@John-McAfeeSorry, but you’re wrong. There is only one situation where you have implied brackets, and that is when you have a numerator and a denominator expressed as a fraction. You evaluate them both separately, then divide. However, in this case, the fact that a 2 is written next to the parentheses without a multiplication sign between them is accepted shorthand for multiplying. The correct answer according to the mathematical rules we invented, and globally follow, is 9. End of.
@giornikitop5373
Жыл бұрын
"and (C), what is he going to do?".
@SpiritmanProductions
Жыл бұрын
Sorry, Dave, but, after expanding the parentheses, I see "n / a(b + c)" as "n / (ab + ac)". It should be no different just because the terms have been substituted with their values. "n / a(b + c)" is not the same as "n / a * (b + c)".
@Gabor-jn9zc
Ай бұрын
You are doing the multiplication before the division and the division before the parens.
@Luminousplayer
Ай бұрын
this assumes that every term after the / belongs in the denominator but that would require another parenthesis to make it explicit for the calculator n/(a(b+c))
@Gabor-jn9zc
Ай бұрын
@@Luminousplayer Assume nothing. Go Left to right. Top to bottom do parens, exp, mult/div, add/sub. I don't get the confusion.
@michaellavalle3843
Жыл бұрын
I fall on the side of the answer is 1. I see it like this. 2(2+1) is a term 2 * (2+1) is two terms A ÷ 2B A ÷ 2(2+1) A ÷ 2(3) A ÷ 6 6 ÷ 6
@jackinthebox301
Жыл бұрын
You'd be completely ignoring the Left to Right of equivalent operations rule to get this answer. So you're still not following the rules properly. Going left to right without solving parenthesis first gets you 6/2 first 3*(2+1) second Even if you want to multiply each term individually you still get 9. 3*2 + 3*1 Anyway you cut it, its still 9.
@michaellavalle3843
Жыл бұрын
@jackinthebox301 @jackinthebox301 The left to right is followed after the terms are completely worked out. See the example above. The 2B is the 2(2+1) term that must be completed. Inside the term PEMDAS is applied, and once that and all other terms are resolved, then PEMDAS is applied to the equation as a hole. Hence, 2B is resolved to 6.
@jackinthebox301
Жыл бұрын
@@michaellavalle3843 But then by your own admission you've simply ignored 6/2 as a term and placed 2(2+1) above it in importance, when they are in fact equal in weight because multiplication and division are the same on the hierarchy. You don't perform M and then D like it is in PEMDAS, they are completed left to right after Parentheses and Exponents are taken care of. Like he says in the video, if you are putting the proper operator in place you will always end up with 9. 6/2*2*(2+1) is the same thing as the 6/2*2(2+1). Edit: your original comment is likewise incorrect. You are lumping together 2B as though that is one object, but it is just shorthand for two different numbers. So the proper expression would be A/2*B. So left to right still applies.
@Hackybaby
5 ай бұрын
@@jackinthebox301 left to right calculation must be an american thing. in germany we do * & / first + & - second.
@jackinthebox301
5 ай бұрын
@@Hackybaby Brother, why are you commenting on this. Especially when you're commenting something I literally talked about multiple times.
@Indsofin
Жыл бұрын
I've always seen this problem as a "notation" problem coming as a consequence of "lazy" writing. Is 6÷2(2+1) defining 6 ÷ [2(2+1)] ("missing the brackets [ ] and specify that the parenthesis operation is in the divisor" to say it somehow ) or 6÷2 x (2+1) (missing a multiplier sign)? Because of ambiguous writing, this problem can be misinterpreted.
@nagyandras8857
Жыл бұрын
Its very easy. ÷ is not a sign of division. It means ratio of 2 things. Stuff left and right of this sign. But its easy to show where dave makes his mistake. 6÷2(2+1) , allright. Lets get rid of those brackets. 2(2+1) =( 2×2 ) + (2×1) = 6 Unless you want to absolutely break mathematics, the correct answer is 1... Implicit operations was a feature in calculators that got removed. So his old calculator is actualy the one that have the correct result.
@Ixions
Жыл бұрын
It seems like it may be a misinterpretation of PEMDAS. Instead of "Parenthesis" it should be "Products"(denoting groups) which aren't complete so long as the "Parenthesis" remains. The trickery is revealed when you write the implied product of your last expression: "6÷2 x 1(2+1)". Products don't exist by themselves. They are a factorized grouping of terms. The factor must be distributed in order to complete the first operation in PEMDAS. Your first expression could be rewritten as 6÷1(4+2) because "one group of 4 and 2" is the same thing as "two groups of 2 and 1" To me this is the failure in reasoning/notation.
@Wylie288
Жыл бұрын
@@nagyandras8857 Everyone actually in mathematics tells you this has two answers. You over simplify. This equation is missing information. That missing information creates two DIFFERENT equations. Thats it. Its that simple. There is two correct answers depending on what you decide that missing information is. PEDMAS does NOT contain any rules for assuming missing information either. According to pedmas this is an invalid equation.
@DigitalOzymandias
Жыл бұрын
The problem is how you view 6÷2(2+1). It actually has been solved by mathematicians both ways, and both are correct depending on the paradigm. If you view it as 6÷2 x n then you are correct, but if you view it as 6÷2n then you are wrong. In most math classes it is expected that you see it as the latter. If we use the standard way of writing it on a computer then it becomes more clear, 6/2n implies it is a fraction 6 over 2n and you would never expect it to be 6÷2×n.
@nagyandras8857
Жыл бұрын
@@Wylie288 everyone with any meaningfull math education will Tell, that first order expressions can only have 1 or 0 solutions. There are no 2 solutions.
@StephenBoothUK
Жыл бұрын
As soon as I saw this I knew what it was going to be. Sorry, Dave, on this one you are wrong, as is your calculator. The issue is implicit vs explicit multiplication. When PEMDAS/BODMAS/BEDMAS/whatever combination you were taught (for me it was BDMSA, which makes me wonder if my maths teacher should be on some sort of register) was created (initially described in a Danish book on gunnery in the early 19th but not codified as a guideline till a maths book published around 1920), as a guideline only, it’s not a rule whatever your teacher in school said, the convention was that you ALWAYS include the symbology so you would never write 6÷2(2+1), it was always 6÷2×(2+1). Multiplication was always explicit. In those circumstances PEMDAS worked fine. Then engineering and other numerate sciences (the STE of STEM) got involved with big equations where dropping unneeded symbols, like the explicit multiplication sign, would let you get more equations on a page. The convention in STE became that implicit multiplication, a number followed by either a variable (e.g. 2x) or a calculation in parentheses (e.g. 2(2+1)), would be calculated with higher precedence than explicit multiplication or division unless otherwise indicated. This, when scientific calculators come out that could have calculations entered with implicit multiplication, was the convention adopted everywhere except North America where a caucus of math teachers kicked up a fuss. When the memes came out I spent some time researching this, hence knowing the history. First off, there is no supreme ruling body in mathematics to set rules so everything you learn is assumptions that have been found to work and guidelines derived from those assumptions that work in the situations they were derived for. PEMDAS, therefore, is only a guideline and one that was derived to handle an environment where multiplication was always explicit. Secondly, 7 billion (people outside the North America) who are taught that implicit multiplication is higher precedence) is bigger than 400 million (people inside North America who are taught dogmatic adherence to PEMDAS). Thirdly, but possibly most importantly, It’s more important that things like rockets work than we soothe the feelings of some teachers who apparently don’t realise that the subject they teach is mathematics, not mathematic. Fourthly Things would be a lot easier if LaTeX was the default way to type mathematical equations. The generally accepted convention is: where possible you should use symbols such as the multiplication sign and parentheses, or layout (LaTeX, you’re on) to make precedence explicit; if the text is in a field where implicit multiplication is king (most STE but more and more M) then give it higher precedence; if in doubt ask the person who wrote it to make it explicit using the methods previously described. Since there’s more calculators used in STE than M they will generally go with implicit multiplication being higher precedence. Unsurprisingly, the Windows 10 calculator pulls the same trick of adding in the multiplication sign the user didn’t enter to make it explicit. Excel complains of a typo then asks you if you want it to insert the multiplication sign. The Microsoft Math app, however, applies implicit multiplication at higher precedence. The problem with your pull it down solution is that in most fields it’s equally or more valid to multiply the 2 into the parentheses to give 6÷(4+2), essentially applying FOIL and treating the 2 as (2+0) so the I and L evaluate to 0. In summary, make things explicit. I suspect that if you were to enter the explicit calculation into your Sharp calculator then it would apply PEMDAS as you want it to. That’s what my Casio calculators (I’ve had to upgrade for additional functionality a few times since the mid 1980s, yes, we’re about the same age, the latest one I have can run Python) do.
@mbp1646
4 ай бұрын
As an engineer myself I am also solidly in the "implicit multiplication takes precedence" category. This is essential when you are dealing with engineering units such as mA and kV. The implicit multiplication by the units and their scaling prefixes takes precedence over everything else. For example 10kV÷10mA=1MΩ if you ignore implicit multiplication and try to apply BODMAS you would incorrectly get 10x1000xV÷10x0.001xA=1VA.
@_d0ser
7 ай бұрын
It's 1 because as written it's the equivalent of 6 / (4+2) because it's a factor of 2(2+1) and factoring is part of the parenthetical section of pemdas. You only get 9 if explicitly add the multiplication sign which isn't present in the original problem.
@nunyabiz1712
5 ай бұрын
Yep, this is an illogical use case he's offered; inserting cardinal values in an algebraic expression and not doing algebra.
@michaelgoldsmith9359
Жыл бұрын
Left to right isn't a law of maths. Implied multiplication is just as valid and is practically the only version used in academia in physics and maths. Treating the left of the ÷ as the numerator and the right of it as the denominator is completely valid and more intuitive.
@John-McAfee
Жыл бұрын
The equation is deliberately imprecise to provoke discussion. It's why even well-educated mathematicians are disagreeing, why different calculators and tools produce different results and why there's still no clear answer even though the puzzle has been floating around for years. If you're asked to perform this calculation for anything more important than a Facebook survey, ask where the equation came from and clarify exactly what was intended. Either add parentheses, rearrange the terms, or format it such that all fractions are unambiguous numerator-over-denominator fractions. 9 or 1 are both valid answers based on interpretation.
@edwinlandy
Жыл бұрын
If I were doing this by hand, I would distribute the '2'. So 6 / 2(2+1) would become 6 / (4+2), or 1. If the multiplication symbol was supplied; 6 / 2 * (2+1) would become 6 / 2 * 3, which is, of course, 9. If I were doing it on a computer, I'd probably assume that it doesn't use the distributive property, which I find primitive.
@fsmoura
Жыл бұрын
oh those mathematicians and their primitive properties!
@okaro6595
Жыл бұрын
You can distribute only after you have agreed on the order. If it was 6 / 2 * (2+1) you could not distribute the 2. You are adding an unnecessary step to hide the decision you made.
@edwinlandy
Жыл бұрын
@@okaro6595 Extra step? The missing operand means distribute. It means the 2 goes with the (2+1). Otherwise, you're just missing an operation. If it's not distribute then why does the missing symbol mean multiplication? Why not division? It could just as easily be 6 / 2 / (2+1).
@edwinlandy
Жыл бұрын
@@okaro6595 If I enter 65 into a calculator and press enter, would it display 30?
@dimon37
Жыл бұрын
While most people consider PEMDAS to be the truth in its highest form, it's actually an approximation. Here's a quote from easily findable article: The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. So, 6/2(2+1) is NOT the same as 6/2*(2+1).
@LuaanTi
4 ай бұрын
And using the same logic, 1/2s doesn't mean half a second, but rather half a Hertz. Wait a minute...
@dimitarnikolov3527
Жыл бұрын
"1" is also correct since implied multiplication has higher priority than regular (explicit) multiplication and division. So: 6/2(2+1)=1 6/2*(2+1)=9
@thatsunpossible312
Жыл бұрын
That’s a rule in older TI calculators - not a mathematical rule.
@stephanszarafinski9001
Жыл бұрын
I was about to say this too, not that I argue that the answer isn’t 9. But I learned at school that the 2 belongs to the brackets part because there is no mulitplier sign. So you complete the entire brackets part including the 2 first and then do the division. Like when the the entire 2(2+1) would be below the 6, under the division line.
@thatsunpossible312
Жыл бұрын
@@stephanszarafinski9001 that would be true… if there were a division line. This is the division sign, so it can’t be made clear what is “under” it. And as Dave alludes to in the video, the division sign hasn’t been equivalent to the line since around 1915.
@HroiG
Жыл бұрын
@@thatsunpossible312 The rule of multiplication by juxtaposition going before regular multiplication or division is used in most mathematics papers and university level math. Its mostly just there because as humans we want to be lazy and be able to write something like 2x/5y without adding the brackets around 5y. But yes, there isn't really one global way of doing mathematical notation, so this can be different between schools. The videos from "The How and Why of Mathematics" on the problem with PEDMAS is a really good explanation of both the disagreement as well as how we got ourselves into this mess, I would highly recommend that video.
@thatsunpossible312
Жыл бұрын
@@HroiG yes, this problem is deliberately misleading. Imagine if students were presented with the distance formula as d = vt + 1/2at^2 Academic papers don’t generally go for ambiguity 😁
@SuperAronGamerMNO
Жыл бұрын
I know people have said this a lot of times, but there is something called juxtaposition. If two things are written together without a multiplication sign, I read them as one thing, such as in 6/2x, and I also apply that to when the factor is written next to parentheses, such as in 6/2(2+1). The thing is that the way math is done is invented by humans, so humans can have preferences on how it's done, and unfortunately, juxtaposition is a subject where people are very divided (no pun intended) on the use of it. It's okay if you think my way of reading it is wrong, but when writing questions, you need to be aware that people can interpret it in different ways, and that's why you shouldn't write the expression like 6/2(2+1). Instead, write it as either 6/(2(2+1)) or (6/2)(2+1), or simply write it as a fraction if doing it on paper. If I want something to be read as being multiplied with a fraction, I usually write it in the numerator, not after the denominator, so I can avoid confusion. So that would be 6(2+1)/2. So basically, when writing expressions like that, you need to be aware that PEMDAS isn't the only way to interpret expressions, and there are ways to write them so everyone gets the same answer. And of course, if you don't like juxtaposition being read first, just write out a multiplication sign. It doesn't take that much effort, but it prevents a lot of confusion.
@flyball1788
Жыл бұрын
Dave's comment about maths not being a good place to have your own rules is very true - but there is enough evidence of juxtaposition taking precedence of normal multiplication that you can't be sure. After 35 years writing various types of code, I always go for the pedantic, but unambiguous method of using parentheses rather than rely on the opinion of the programmer who wrote the parser.... but I'm a H/W engineer so I never rely on the programmers anyway 😜
@evgen5647
Жыл бұрын
@@flyball1788 Prior to 1900 the rule was as follows. If multiplication sign is ommited, then the multiplier is unconditionally associated with adjacent parenthesis. Please hear me out, they used this rule in academic papers and scientific work in XIX and XX centuries. Moreover, this rule is still applied in some contries e.g. Russia, ex-USSR, and I believe Great Britain as well. The PEMDAS rule is a simplification in a nut shell. It is a mnemonic to help people to remember the "correct" order of operations. Except it actually doesn't tell you what to do if multiplication sign is ommited. In case your math teacher tought you "If you don't see multiply sign just imagine it is there and then apply PEMDAS rule", he is just wrong. Regarding calculators, despite the fact lots of modern software calculators give 9 as an answer, there are scientific calculators which still will give you 1 as an answer. Modern mathematitians, knowing that the default assumption would be different in different countries, recommend to use explicit multiplication sign in those cases where it will be ambiguity otherwise.
@okaro6595
Жыл бұрын
@@flyball1788 Writing code and writing math are different things.
@okaro6595
Жыл бұрын
@@evgen5647 The issue has nothing per se to do with parenthesis. Parenthesis is just the thing that allows implied multiplication. You just cannot use it between two numbers. More often it is used with variables.
@evgen5647
Жыл бұрын
@@okaro6595imagine we replaced all numbers with variables like this: a÷b(c+b)=? Does it remove the ambiguity? No it doesn't! For some reason you think that the rules for arithmetics and the rules for algebra differs. They don't!
@Gunbudder
Жыл бұрын
i love this problem. they way it was explained to me by the professor that showed it to me is that the question is really asking what exactly the in line division symbol means and how it works with order of operations. and to my surprise, my professor told me there is NO CORRECT ANSWER! Instead he explained this is why we never use the inline division symbol anymore. it is effectively a non-standard symbol with some debate on how exactly it works (similar to the debate on if 0 is a natural number or not). and you can find text books that support both answers here. some say to always multiply before dividing when using inline division symbol, and some say to follow left to right always with parenthesis, then exponents, then multiply OR divide as read left to right, then add or subtract as read left to right. and i've even found examples in a text book that show to convert the inline division symbol into a standard fraction notation before doing anything at all which is a weird third option. all that said, i maintain that the correct answer to 6÷2(2+1) is false or invalid because ÷ is not a valid math symbol. if instead you write 6/2(2+1), then it is clearly just a matter of which calculator engine you use and if it does strict PEMDAS or left to right when you leave out parens. For what its worth, wolfram alpha will take 6/2 as an irrational number and do an implied multiplication which is the standard method. i was taught long ago that a lack of parens after the / symbol means that the / symbol applies to exactly the next term only (in this case a 2). or more specifically, that / only affects the next single term and never includes implied multiplications
@tonymouannes
Жыл бұрын
That doesn't apply to implied multiplication, which takes precedence over multiplecation and devision. Someone else explained why in another comment. Basically 2(2+1) is the same as 2y and 2y or 2x, or whatever, which is always treated as one entity.
@GordieGii
Жыл бұрын
But the discrepancy arises from the brackets, not the division. You see 2 * (2 + 1) ≠ 2(2 + 1) 2 * (2 + 1) = 2 * 3 2(2 + 1) = (4 + 2)
@Xnoob545
Жыл бұрын
@@GordieGiino???? Brackets come first 2(2+1) = 2(3) = 2x3 = 6
@Xnoob545
Жыл бұрын
@@GordieGiithere would only ever be a 4 if it was 2(2) + 1 = 4 + 1 = 5
@lyrimetacurl0
Жыл бұрын
@@Xnoob545 in Maths it's okay to go from 2(1+2) to (2+4) because you multiplied the individual parts by the outer part.
@Sparlock42
6 ай бұрын
The expression is ambiguous, as implied multiplication by juxtaposition is often taught as having a higher precedence, and you will often find this rule followed in physics textbooks, for example. The multiplication by juxtaposition is implicitly showing grouping. That is, 6/2*(1+2) and 6/2(1+2) are communicating two different ideas. This rule actually works better in the real world. For example, take this system of equations: y = 6/2x x = 2 + 1 I expect that most people attempting to solve this system of equations would give the value of y as 1. Assuming that you insist PEMDAS should still be followed in this particular case, I would point out that: 6*x/2 and 6x/2 and 6/2x and 6/2*x would all be identical, but the only way to notate my intended meaning would be 6/(2*x) or 6/(2x). This is both confusing and inefficient. It's worth mentioning that, while I am an idiot, there are numerous papers, statements from mathematical societies, and real world examples that would agree with me.
@PatrikBergsten
Жыл бұрын
‘The Why and How of Mathematics’ has a couple of good videos about PEMDAS and Multiplication by juxtaposition. She says that PEMDAS is the oversimplification taught to children but PEJMDAS (J = Multiplication by Juxtaposition) is what is expected when getting to University/Academia and what you’ll find in scientific papers. Calculator manufacturers ask teachers how they like the order of operations to work, apparently they go back and forth from year to year.
@marianneoelund2940
Жыл бұрын
That puts academia at odds with accepted computing conventions. To be honest, until today I had never even heard of assigning a higher precedence to juxtaposed parenthetical terms. I can see the utility, for example in engineering we often have transfer-function expressions such as [(s+1)(s+3)]/[(s+2)(s^2+10s+100)] and the juxtaposition rule would allow it to be written without the brackets. However, I believe the rule just causes confusion and misinterpretation (not to mention argumentation) and I'm now wishing it never existed!
@jen204
Жыл бұрын
@@marianneoelund2940 Except that in computing, you would never interpret 4x ÷ 2x as 2x^2, you of course treat it as 2 (oops, I had 2x before! Edited to fix). That is the same concept as the implicit multiplication described above. PEJMDAS keeps us consistent with how we interpret statements with variables ... as it must, because mathematics depends on being able to substitute portions of an equation with arbitrary equivalents, including variables defined to be equivalent.
@nujuat
Жыл бұрын
@marianneoelund2940 except implicit multiplication doesn't really appear in computation. Like Dave had to explicitly put it in himself for most of the video.
@taz030485
Жыл бұрын
I feel the problem with all these kinds of problems stems from the division operator being written on a single line, as opposed to how it’s written in advanced math classes, because then the divisor is cleanly what is below the line.
@satibel
Жыл бұрын
@@ThomasVWormalso it depends what's your background, in some places the implicit multiplication is considered as having implicit parentheses. Like if you go 6/2x it's implied that it's 6/(2*x) and if you actually want (6/2)x you'd just write 6x/2
@Philafxs
Жыл бұрын
@@ThomasVWorm There is a bit of an issue in that / also is a single-line fractional notation, the less ambiguous division operator being ÷ (which low and behold represents a fraction too, but at least it wouldn't make for any fractional notation). Therefore, the math problem as given in the beginning of this video is correct, but with how it's noted usually and even later in the video, as 6/2(2+1), it's deemed truly ambiguous. Besides that different priority systems still in use internationally could still make for different solutions.
@cthecheese1620
Жыл бұрын
@@ThomasVWorm The world has never worked off of one clear set of rules. Different industries have different standards because the context is different. Why try to shove everyone in one box?
@Philafxs
Жыл бұрын
@@ThomasVWorm The spaces would probably indicate it's not a fraction, but in a multi-line notation there is nothing wrong having multiple levels. The kind of line could make a difference though. As a single line there's no difference between 1/2/3 or 1÷2÷3 or 1/2÷3, but it could also be 1÷2/3 in which case one would write it like that or as 1/(2/3).
@alastairbishop2450
Жыл бұрын
The great thing about standards is that there are so many of them.
@andrewkepert923
Жыл бұрын
Neither answer is wrong.* It's the question that is wrong. Usually, the point of communication is to be unamibiguous. In this case, communicating the steps required to figure out a number. These stupid PEMDAS/BODMAS puzzles are merely bad communication in a context where there are other less ambiguous ways of asking the same question. It is like saying "I like listening to Dave and eating". Do I like both listening to Dave and listening to eating? Do I like listening to Dave while eating? Do I like listening to Dave and also like eating? Since it's unclear, I'll choose a better form of words. Whichever calculation is intended, formulating the question to remove ambiguity is trivially easy, so do that, and we shouldn't treat this as any more profound than that. (* - but the only possible right answer is 9 - as Dave says, it's silly to have two semantially distinct versions of one operation, yet only one version of the other three.)
@papa_smerf7603
Жыл бұрын
google PEJMDAS, you may be shoked
@Mezz9009
6 ай бұрын
The problem here is the laziness to i ignore the significance of implied vs implicit. We literally coded calculators around the fact that lesser intelligible teachers only wanted to teach simpler math. L->R multiplication division should've been excluded all together as it doesn't properly visualize problems. PEMDAS enforces all equations must be written lateral, PEJMDAS allows written equations to express multiple fuecets/dimensions/applications.
@georgephilippe4028
Жыл бұрын
PEMDAS says nothing about omitted but "implied" operators. The way the problem is written determines the result. Omitting the * between the 2 and the parenthesis is simple sophistry that confuses an otherwise simple operation. Decades ago it was taught that an expression like 2(2+1) has to be solved first, as it is part of the parenthesis group, then that result is divided into 6, equalling 1. The expression: 6/2*(2+1) is altogether different, and the PEMDAS rules can then be applied. My scientific calculator does exactly that... omitting the * results in the answer 1. Using the * gets 9. It's confusing, and that's why RPN is better.
@normanross3422
3 ай бұрын
Indeed. For PEDMAS to be "right" it ignores basic arithmetic foundational corner stones such as the Distributive Law. Unfortunately things have to be dumbed down today because most everybody seems to have become dumber since the 1970s.
@dogoku
Жыл бұрын
The calculator is not wrong, it is simply using a different convention (PEJDMAS) to interpret the expression, because it is ambiguous. There are a lot of videos on KZitem by mathematicians that explain what is actually happening. A bit more research wouldn't hurt...
@bobafettjr85
Жыл бұрын
I just watched a video about that exact thing last night.
@JxH
Жыл бұрын
Search KZitem: PEMDAS is wrong Many videos by Maths PhDs PEMDAS by itself is buggy when worshipped.
@bobafettjr85
Жыл бұрын
@@ThomasVWorm but the "bad practice" existed before calculators. It's more a failing of the American school system.
@cassiee.3969
Жыл бұрын
@@ThomasVWorm You're so close to getting it. You're just confused about which "rule" is new and which is old. I put rule in scare quotes because none of this is actually rules, it's all notational conventions. PEMDAS originated as a mnemonic to help remember the convention, but it left out a step. Oops. And now there are a lot of people who learned the convention from the mnemonic. Which means there are two conventions. One is used by mathematicians and scientists. The other is used by schoolteachers, schoolchildren, and people younger than 50 whose mathematical education ended at that level. If that sounds like it's a mess, that's because it is.
@bobafettjr85
Жыл бұрын
@ThomasVWorm The question is what are the rules? Clearly PEMDAS isn't the end all be all of else some mathematicians wouldn't use PEJMDAS. People were taught different methods in different areas. Certain things are absolutely true in math A=A, 1+1=2, the area of a circle is πr². If there is a proof that sets the order of operations then this wouldn't be something people still squabble over. I think the biggest issue with this is notation. 6÷(2(1+2)) is clearer than 6÷2(1+2). Also there's ÷ vs / to some people everything after / is a denominator. So I do think mathematicians should hold a council and figure out official definitions. If they can get together to decide Pluto isn't a planet they can decide an official order of operations.
@biloki3079
Жыл бұрын
PEMDAS doesn't always apply. The Math professors that I have looked up all agree the answer is 1, and explain why.
@akdm82
Жыл бұрын
Perhaps you should explain here because your comment alone isn’t proof
@biloki3079
Жыл бұрын
@@akdm82 Fair. Here is the complicated answer. While the numbers are different, it's the same equation with the same argument. Order of arithmetic operations; in particular, the 48/2(9+3) question. A problem that hit the Internet in early 2011 is, "What is the value of 48/2(9+3) ?" Depending on whether one interprets the expression as (48/2)(9+3) or as 48/(2(9+3)) one gets 288 or 2. There is no standard convention as to which of these two ways the expression should be interpreted, so, in fact, 48/2(9+3) is ambiguous. To render it unambiguous, one should write it either as (48/2)(9+3) or 48/(2(9+3)). This applies, in general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc). In contrast, under a standard convention, expressions such as ab+c are unambiguous: that expression means only (ab)+c; and similarly, a+bc means only a+(bc). The convention is that when parentheses are not used to show the contrary, multiplication precedes addition (and subtraction); i.e., in ab+c, one first multiplies out ab, then adds c to the result, while in a+bc, one first multiplies out bc, then adds the result to a. For expressions such as a−b+c, or a+b−c, or a−b−c, there is also a fixed convention, but rather than saying that one of addition and subtraction is always done before the other, it says that when one has a sequence of these two operations, one works from left to right: One starts with a, then adds or subtracts b, and finally adds or subtracts c. Why is there no fixed convention for interpreting expressions such as a/bc ? I think that one reason is that historically, fractions were written with a horizontal line between the numerator and denominator. When one writes the above expression that way, one either puts bc under the horizontal line, making that whole product the denominator, or one just makes b the denominator and puts c after the fraction. Either way, the meaning is clear from the way the expression is written. The use of the slant in writing fractions is convenient in not creating extra-high lines of text; but for that convenience, we pay the price of losing the distinction that came from how the terms were arranged horizontally and vertically. Probably another reason why there is not a fixed convention for order of multiplication and division, as there is for addition and subtraction, is that while people frequently do calculations that involve adding and subtracting lengthy strings of numbers, the numbers of multiplications and divisions that come into everyday calculations tends to be smaller; so there is less need for a convention, and none has evolved. Finally, the convention in algebra of denoting multiplication by juxtaposition (putting symbols side by side), without any multiplication symbol between them, has the effect that one sees something like ab as a single unit, so that it is natural to interpret ab+c or a+bc as a sum in which one of the summands is the product ab or bc. Without that typographic convention, the order-of-operations convention might never have evolved. When one has numbers rather than letters, one can't use juxtaposition, since it would give the appearance of a single decimal number, so one must insert a symbol such as ×, and there is less natural reason for interpreting 2 × 3 + 4 as (2 × 3) + 4 rather than 2 × (3 + 4), but I suppose that we do so by extension of the convention that arose in the algebraic context. Likewise, because addition and subtraction constitute one "family" of operations, and multiplication and division another, and perhaps also because the slant "/" doesn't seem to separate two expressions as much as a + or − does, we are ready to read a/b+c etc. as involving division before addition. But when it comes to a/bc, where the operations belong to the same family, the left-to-right order suggests doing the division first, while the "unseparated letters" notation suggests doing the multiplication first; so neither choice is obvious. It is interesting that in the 48/2(9+3) problem, the last element was written 9+3 rather than 12. If the latter had been used, it would have been necessary to insert a multiplication sign, 48/2×12, and I would guess that a large majority of people would have then made the interpretation (48/2)×12. Perhaps we will never know where this puzzle originated; perhaps it was cunningly designed so that one interpretation would seem as likely as the other; or perhaps it came up as a real expression that someone happened to write down, not thinking of it as ambiguous, but that other people did have trouble with. From correspondence with people on the the 48/2(9+3) problem, I have learned that in many schools today, students are taught a mnemonic "PEMDAS" for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If this is taken to mean, say, that addition should be done before subtraction, it will lead to the wrong answer for a−b+c. Presumably, teachers explain that it means "Parentheses - then Exponents - then Multiplication and Division - then Addition and Subtraction", with the proviso that in the "Addition and Subtraction" step, and likewise in the "Multiplication and Division" step, one calculates from left to right. This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation for a/bc, namely, (a/b)c. But so far as I know, it is a creation of some educator, who has taken conventions in real use, and extended them to cover cases where there is no accepted convention. So it misleads students; and moreover, if students are taught PEMDAS by rote without the proviso mentioned above, they will not even get the standard interpretation of a−b+c. Should there be a standard convention for the relative order of multiplication and division in expressions where division is expressed using a slant? My feeling is that rather than burdening our memories with a mass of conventions, and setting things up for misinterpretations by people who have not learned them all, we should learn how to be unambiguous, i.e., we should use parentheses except where firmly established conventions exist. If expressions involving long sequences of multiplications and divisions should in the future become common, then there may be a movement to introduce a standard convention on this point. (A first stage would involve individual authors writing that "in this work", expressions of a certain form will have a certain meaning.) But students should not be told that there is a convention when there isn't. Incidentally, it is worth noting that in certain cases, no convention is needed. The meaning of a+b+c is unambiguous even without the "left-to-right" convention, by the associativity of addition, and similarly abc by associativity of multiplication. By further properties of the operations, the values of a+b−c and ab/c come out the same whichever order one uses. In contrast, a−b+c and a−b−c require the "left-to-right" rule, while in the absence of a corresponding rule for multiplication and division, a/bc (as discussed above), and likewise a/b/c, are ambiguous.
@selseyonetwenty4631
3 ай бұрын
Just as a point of information, my Casio fx-85gt gives the answer 1 if the 'x' is omitted, 9 if included. The user guide explicitly says it will do this, it has a precedence table and 'multiplication where multiplication sign is omitted' is listed as higher priority than other multiplication and division, so the design is deliberate, not a software bug.
@GanonTEK
3 ай бұрын
Yes, you're right. Depends on the scientific calculator but here are some that give one or the other: These give 1: Casio FX 83GTX, Casio FX 85GT Plus, Casio 991ES Plus, Casio 991MS, Casio FX 570MS, Casio 9860GII, Sharp EL-546X, Sharp EL-520X, TI 82, TI 85 These give 9: Casio FX 50FH, Casio FX 82ES, Casio FX 83ES, Casio 991ES, Casio 570ES, TI 86, TI 83 Plus, TI 84 Plus, TI 30X, TI 89. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation which implies grouping (1). Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation (1). TI later changed to the programming/literal interpretation (9) but when I asked them were unable to find the reason why. Some commenters have said it was pressure form American teachers but I've no confirmation of that. So, yes, features not bugs.
@runforitman
Жыл бұрын
this is why i am in the habit of surrounding everything in parentheses to make sure it calculates the order im expecting
@nickwallette6201
Жыл бұрын
This is my philosophy in C, whether the expression is arithmetic or logical. What's the strictly defined order of operations? Who cares. Don't leave it ambiguous and it doesn't matter.
@jbird4478
Жыл бұрын
@@nickwallette6201 Depends. An expression like x + 2 * y is perfectly clear on it's own. Though I'd use whitespace there: x + 2*y. I've heard people argue for adding parentheses because others might not know the order, but I think you should be expected to know that as a programmer. It is never ambiguous, regardless of how you write it. Parentheses can help readability by visually grouping things together though.
@nickwallette6201
Жыл бұрын
@@jbird4478 That last bit is my entire point. :-) I know you _should_ know the order, and there _should_ be a single correct answer. And in the case of a simple arithmetic expression like that, sure. But... I still use parentheses out of habit, intentionally formed habit, to ensure that there's never a time (particularly more with logic expressions) that would be implementation-defined, or difficult for a reader (like myself, 5 years later) to parse. If nothing else, it just relieves your brain of having to sort through it. It's spelled out for you. Mistakes happen, and anything I can do to minimize the chance or severity of those -- it's a good thing. :-)
@jbird4478
Жыл бұрын
@@nickwallette6201 My point is that it is _never_ implementation-defined or ambiguous. The order of operations is fully defined by the standard. x || y && z will always parse as x || (y && z). That should not cause any confusion. The risk in always using parentheses is that it will cause you confusion if you encounter code from people (like me) who assume this is understood. I do use extra parentheses sometimes, but that's more in the same way as one uses whitespace; to give some visual structure that makes it easier to skim through the code.
@nickwallette6201
Жыл бұрын
@@jbird4478 I'm not going to argue about this. I recall at some point reading a text book on C that mentioned some combination of pointer dereferencing or something like that, that was evaluated differently on two different compilers. I can't back that up, because I don't remember what text it was, so feel free to take that with a grain of salt. The point the author was making, and the point that _I'm_ making, is that _usually_ there is one single correct answer. And sometimes evaluating what that answer is, is enough to make somebody give up and move on. I don't care whether it is, is not, or "shouldn't be" ambiguous. If it's even one millisecond faster and thus easier for a human being to parse (x + y) * (a + c), then I'll write it that way, because at least on my keyboard, I have unlimited parens, and they're free. For trivial examples, it hardly matters. For more complicated examples, it matters more. So I do it everywhere, and never have to think about whether it would be helpful to add hints. They're just there. Feel free to ignore them if they're superfluous.
@robertjfrey6063
Жыл бұрын
I remember being exposed to RPN (reverse Polish notation) in the 70s when I first picked up an HP calculator. It took about 30 seconds before I heard angels singing and I realized that I had the only rational system for performing calculations on the fly. You characterized RPN’s stack-based entry system as forcing the user to “ translate” computations. For me it was simply the way I visualized them. Now ~50 years later with a PhD in applied math and using Mathematica as my primacy programming environment, I continue to use RPN calculators and view those using so-called CAS (computer algebra systems) calculators with a combination of pity and horror.
@nneeerrrd
Жыл бұрын
Ok, we got it. You are so much better than us.
@jchavins
Жыл бұрын
yeah.....God I hate TI calculators. My favorite was the HP55.....but I loved my 25C also and it was a lot cheaper....on my laptop and desktop I have a 55 emulator...my phone has the 25C
@chitlitlah
Жыл бұрын
I was first given an RPN calculator for a competition in high school. I didn't do so well in the competition because I couldn't thoroughly learn RPN in time, but I came back to it later and never went back to algebraic notation. Algebraic notation is obviously more like how we'd write a problem, but I think RPN is more like how we'd do it in our heads. (4+5)/(1+2) "Take 4. Add 5. Take 1. Add 2. Divide the last two results." If you put the verb after the noun like you're speaking Japanese, you get almost exactly what you'd type on an RPN calculator. 4 [enter] 5 + 1 [enter] 2 + /
@rkadowns
Жыл бұрын
This can easily turn into a Linux vs. Windows debate, but really RPN is objectively superior, like Betamax. Shame it did not become the standard.
@GordieGii
Жыл бұрын
@@rkadowns Yup. Sony really screwed up by selling VHS to JVC before Betamax was ready to launch. (to recoup their R&D money) It's amazing what 6 months can do when the public and content publishers are chomping at the bit.
@SkippiiKai
Жыл бұрын
Not even one mention of the distrubitive law of mathematics? The one that says any time you have a number multiplied by a sum in parentheses like 2(2+1) has to have the same anser is if it was calculated as (2*2 + 2*1). It seems like that fact from 8th grade algebra really needs to be discussed here, as it's fundamental to the issue. As you said, if math isn't something you should play by your own rules, the distrubitive law or distributive property should be included. And if zi sound angry, I assure you I'm not, it's just that I've been agonizing and losing sleep over this for months and when I saw this video from you show up, I thought today would be the day I can finally rest again. I love your channel Dave. Please help me understand.
@actually_it_is_rocket_science
Жыл бұрын
The thing is you're confusing two different things. PEMDAS is separate from where you use distribution. Distribution is typically useful when dealing with unknowns and simplification.
@actually_it_is_rocket_science
Жыл бұрын
For distribution to apply here it would have to be 6/(2*(2+1)) as now the 2 isn't utilized in a higher priority step.
@actually_it_is_rocket_science
Жыл бұрын
@joshknight1620 correct but only if the 2 is not involved in a higher priority expression such as the 6/2 in this example. The 2 cannot be distributed because of that.
@nilfox921
Жыл бұрын
Its the difference between arithmetic and algebraic rules
@angeldude101
Жыл бұрын
It is more than possible to use distributivity for 6 / 2 * (1 + 2). You just need to also acknowledge commutativity and that "right-to-left" is bullshit. What do you want me to distribute? I can give you 6 * (0.5 + 1) or / 2 * (6 + 12), but that last looks weird with nothing before the division so lets fix that: (6 + 12) / 2. Much better. Or I can just distribute both factors and get (3 + 6). Now to apply the parentheses rule having done everything else in exactly reverse order and get 9.
@maro-soft
Жыл бұрын
The way I was thought about it is to use a rule of implied multiplication (juxtaposition). So if there is no symbol between the number and perentheses, it means you need to multiply what is inside of it by that number first before doing any other calculations.
@JoshuaKA02
Жыл бұрын
I was first taught this too, but it becomes even more important for higher maths. To me it's simple to see this as it's written. If they wanted it the other way they would have written the multiplication sign. I've always seen it as distributive multiplication, and that will never change; that's what it is.
@wodmarach
Жыл бұрын
Yeah PEJMDAS is the more accurate mnemonic but the US for some reason doesn't seem to teach juxtapose first... so for most of the world the 1 answer is correct.
@leesaudan
Жыл бұрын
Agreed. Otherwise, x/2x would not be one half (for non-zero x), but x/2*x = half of x squared instead!
@puntura
Жыл бұрын
@@leesaudan they have never come to this point they are solving elementary school math. to confuse more than half the population that did not take higher math classes so than they can argue. If the teacher had taught well we should have seen such video.
@WilliamWizer
Жыл бұрын
and that's clerly wrong. here is a nice expression for you (2+1)3^3 what is it's value? you won't find a single calculator that solves it as (2+1)3^3=(3)3^3=9^3=729. either you can't imput the expression or they solve it as (2+1)3^3=(3)3^3=(3)27=81. that breaks the rule you were taught. you didn't multiply what is inside of the parenthesis by the 3 before doing any other calculations. that rule works fine when you are using fractions and superscript to represent powers because the size and position of the numbers removes any possible confusion. when you are forced to use a single line without superscript or subscript, the rule breaks. multiplication is commutative. having a parenthesis (implicit multiplication) before or after gives the same result. which means (2+1)3^3 and 3^3(2+1) are equal.using superscript makes it easier to see since it becomes (2+1)3³ or 3³(2+1)
@NovaCyn
Жыл бұрын
Not only did my dad indeed swear to an old HP calculator using postfix notation, he managed to get me hooked on the nicely unambiguous notation which also removes the need for parentheses. I even have an RPN calculator app on my phone today!
@waynenewark5363
Жыл бұрын
I have a RPN calculator app on my phone and I still have my HP 11C calculator too. I just wish I had bought a HP 16C at the time.
@PJElliot
Жыл бұрын
Try the Free42 or the updated Plus42 calculator - available on most platforms - which implements the HP-42S calculator.
@thomasmaughan4798
Жыл бұрын
Same here, HP41C emulator on Android. I wish I had never gotten rid of my actual HP41C. I still have an original HP-35. Slower than molasses on a winter day but when it was first marketed, it was the most amazing thing since sliced bread.
@markthompson2874
Жыл бұрын
It is 1, implicit multiplication comes before explicit division. Most anyone would say x / 2x equals 1/2. Based on your logic it would equal x^2/2.
@laurendoe168
Жыл бұрын
Please show me where there's a difference between "implicit" and "explicit".
@casse82
Жыл бұрын
Yes, this was the way it was taught back in the day (at least in some countries) and it was correct and is correct when following that rule. However that rule has since been changed and now implicit and explicit multiplication are equal in priority. I was also taught the old way.
@nilfox921
Жыл бұрын
You're right in saying x/2x is equal to 1/2, but only because the 2x element is a reciprocal. The difference in / and ÷ is that elements affixed to ÷ have to be converted to ×(reciprocal) to work with algebraic rules.
@markthompson2874
Жыл бұрын
@@casse82 And it still is a valid way of doing a problem. The problem with this specific problem is that there's no way to know which convention that they are intending on using. Generally most people you stop using the obelus before you even get into order of operations and start using the fraction bar and visual location to make it more obvious.
@casse82
Жыл бұрын
@@markthompson2874 Well the consensus nowadays is that the default is to follow PEMDAS. The old way is generally now valid only if it's specifically defined to use that OR if it's used as a convention in the context that you are in (your workplace, your basement etc.).
@ZapAndersson
Жыл бұрын
Of all people I wasn't expecting YOU to be this wrong, Dave. What you are missing is PEJMDAS, where "J" stands for "Juxtaposition" (meaning, "multiplication by juxtaposition", i.e. when you do not put in the multiplication sign). This beats the MD level. Let me put it this way to make it simple. If I assign x=1+2 and then tell you to compute 1/2x do you still seriously get 9? Basically the error you repeat is putting in the explicit multiplication sign, which indeed results in the answer 9. You are testing it with broken calculators that cannot handle juxtaposing multiplication, which has higher priority. PEMDAS is a rule for small children. THe true rule is PEJMDAS. Any ACTUAL mathematician would write this expression with the 6 on top, a horizontal line under it, and 2(1+3) under, so for them this problem doesn't occur. The only reason we have this nonsense discussion is that regular humans can't write LaTeX :)
@actually_it_is_rocket_science
Жыл бұрын
See but you're also assuming that it's 6/ all of that not 6/ 2* the rest. That's the problem with this notation. It's just imprecise because we have the division in there. You really should add more context. People like to add the whole juxtaposition thing but when you look at equations that use the juxtaposition it still typically follows PEMDAS because anybody who's using juxtaposition typically is writing the equation without ambiguity. As soon as there's any debate over the equation, it's a bad equation.
@johanlarsson9805
Жыл бұрын
@@actually_it_is_rocket_science There is no assuming, and no, it is not "6/all of that". The longer expression "6/2(1+2)+4-2" would not have the "plus four minus two" part in the division. Its the fact that the 2 is coupled to the parenthesis that makes it stronger than a simple 2*parenthesis. When written like that anyone experienced with math would think of it as a single unit, and the unit is 2parenthesis. A good example is a/bc which would ALWAYS mean a over bc. a/bc+5 would mean a over bc then add 5.
@ZapAndersson
Жыл бұрын
@@johanlarsson9805 Exacatly. Go back to my example where we assign x = 1+3 and we then do 1/2x ... I say that is distinctly different to 1/2*x ... you can't just take a multiplication-by-juxtaposition and replace it with a multiplication sign, without wrapping the juxtaposed entities in parenthesis. I.e. everybody agrees 1/2x is 1 / (2*x). When you unjuxtapose, the juxtaposed pair gets parenthesis implicitly.
@0LoneTech
Жыл бұрын
@@ZapAnderssonIt's not quite as simple as that. a/bc² = a × b⁻¹ × c⁻²
@ZapAndersson
Жыл бұрын
@@0LoneTech Agreed that would mean a / (b * c *c) which is equivalent to what you wrote. But the PEMDAS people here want it to be (a / b) * (c * c), which is obviously wrong. They are all simply wrong, @dave included
@parkloqi
3 ай бұрын
9:05 “for operators of equivalent precedence you proceed from left to right” Except exponentiation, which is right-to-left.
@CiscoWes
Жыл бұрын
The calculator that said 1 is the correct answer is right. The reason why is multiplication by juxtaposition takes priority over the whole PEMDAS thing. For example… take a/bc. Following PEMDAS strictly, you would end up with a/b*c. The juxtaposition of b and c take priority. It would be a over bc or a divided by bc. The confusion over this very problem is all over the internet and there’s several good videos explaining the multiplication by juxtaposition.
@notenoughmonkeys
Жыл бұрын
I still think my favourite one is this delightfull troll expression: 230 - 220 * 0.5. You may not believe it, but the answer is actually 5!
@Gameboygenius
Жыл бұрын
And that's a fact(orial)!
@JxH
Жыл бұрын
6 _________ = 1 2(2+1) Long horizontal fraction bars do not respond well to PEMDAS. They're commonly used in scientific and mathematics journals and papers. Applying PEMDAS mindlessly is not recommended. Best to avoid ambiguous notation. Long horizontal fraction bars leave no room for misinterpretation, and yet do not follow PEMDAS. Yes, ...I can anticipate that some will mention invisible brackets, but why did I have to mention this point first? That's the point, PEMDAS is silent on this important counter example. PEMDAS, by itself, is clearly defective. Do not worship it.
@Islandwaterjet
Жыл бұрын
You are correct and you beat me by 8 minutes. Funny we are the only two here to be the outliers.
@Aderaen
3 ай бұрын
Long bars work like this 6/(2(2+1)) they are essentially just hiding ( ) exacly like 2(4+1) hides 2x(4+1) so it still applies
@JxH
3 ай бұрын
@@Aderaen You must be pretty naïve if you actually believe that anyone would accept your flimsy explanation.
@nomore6167
24 күн бұрын
The problem isn't PEMDAS. The problem is implied operators. Parentheses don't explicitly mean multiplication, but rather multiplication is implied when there is a lack of operator before the parentheses.
@JxH
24 күн бұрын
@@nomore6167 The problem is, as it always is, people. In this case, those that worship at the feet of PEMDAS without understanding the bigger picture. "Some understand the rule; real experts understand the exceptions." Cheers.
@probablynotmyname8521
Жыл бұрын
It should be noted that google is “inserting” the operator because its walking the expression tree that it builds and spitting out what the tree holds. The insertion is happening at the parse and tokenize time, probably when it sees an opening bracket following a number.
@wolfblaide
Жыл бұрын
The issue is more that there are implied parenthesis around the 2(2+1), its a standard shortcut. This is why the answer of 1 is actually considered the right answer in most scenarious, not what the calculator tells you. The old Sharp calculater gets it more right, although possibly for the wrong reason. You're just expected to know the implied shortcut is there, and to deliberately ignore the PEMDAS/BODMAS rule when its written like this.
@davestorm6718
Жыл бұрын
Actually, is not an implied parenthesis at all - the number immediately to the left parenthesis is ALWAYS the multiplier of what's inside the parentheses. a(b+c) = ab + ac though one might argue that the initial 6 is part of the multiplier so 6/2 * (2+1) or 3*(3) = 9, but this would violate the P first rule so the division symbol would not be counted since it is not textually adjacent to the parentheses group. Variable substitution would make this very clear.
@darkdudironaji
Жыл бұрын
There are no implied parentheses with a ÷ symbol. There are only implied parentheses when written as a fraction. With the division symbol parentheses MUST be explicit.
@theantipope4354
Жыл бұрын
No. There are no 'implied' parens anywhere. They are not a thing.
@wolfblaide
Жыл бұрын
@@darkdudironaji Nope, the parentheses are always implied. The convention is to apply the multiplication first in this case, before the division. That's why no-one comes up with the answer of 9. 9 is the PEMDAS/BODMAS answer, 1 is the conventional answer.
@wolfblaide
Жыл бұрын
@@theantipope4354 You're gonna run into difficulties reading pretty much any non-shool level math then.
@wyldanimal2
Жыл бұрын
Sorry Dave, but the correct answer is 1, Juxtaposition takes Priority over Multiplication and Division. It should be called PEJMDAS, not just PEMDAS You should always put in the Missing Brackets in the equation. 6/2(2+1) should be expanded to 6/(2x(2+1)) Always put the missing brackets in where there is a Juxtaposition.
@John-McAfee
Жыл бұрын
6/2(2 + 1) = 6/[2(2 + 1)] = 1 is juxtaposed [and implicit]. 6/2 (2 + 1) = (6/2) (2 + 1) = 9 is implicit but not juxtaposed. 6/2 × (2 + 1) = (6/2) (2 + 1) = 9 is explicit multiplication.
@John-McAfee
Жыл бұрын
There isn't a proper answer due to the nonsense syntax of the statement
@wyldanimal2
Жыл бұрын
If the equation was instead 6/2( X+Y) you would get 6/(2X+2Y) expanding the Juxtaposition with Brackets you would expand it to 6/(2x(X+Y)) which equals 6/(2X+2Y ) So doing the same with 6/2(2+1) you expand and get 6/(2x(2+1)) which is the same as 6/(2x2+2x1) = 6/(4+2) = 6/6 = 1 PEJMDAS
@John-McAfee
Жыл бұрын
@@wyldanimal2 I would have answered this as 1 in 5th grade and gotten it correct. I agree, but think there is not a universally recognized convention for evaluating this expression.
@robertcolpitts4534
Жыл бұрын
Appreciate your comments on the RPN calculator. Once I started using one, I never looked back. Most of the younger engineers don't use one anymore so when they grab mine, they can't figure out how it works! 😂😂😂
@wictimovgovonca320
Жыл бұрын
My calculator in college was the HP-29C, at the time the most popular non-RPN calculator was the TI-51. I don't remember if we ever checked what the TI did with the above expression, but I remember being able to enter complex expressions much faster than those who used the TI model. b.t.w., both of the above calculators were programmable. The one advantage the TI offered is those programs could be saved (or purchased) on small magnetic cards. Of course my programs would not be lost when I turned off the power so I didn't need those cards, although I was limited to 99 steps.
@melkiorwiseman5234
Жыл бұрын
I still have an old RPN calculator. I was surprised at how quickly I picked up on how to use a calculator without an equals key, and how easy it is to use once you know how. It also has a "program memory" which is just automatic button pushing, with each button push occupying one memory space (I think it has 64 total). It even has a "halt" feature which pauses a program so you can enter another number before continuing the program.
@thomasmaughan4798
Жыл бұрын
I love RPN.
@robertcolpitts4534
Жыл бұрын
@@melkiorwiseman5234 - Did a lot of programming on an HP-28S (which I still have). It's retired since I replaced it with an HP-50g. That's my day-to-day work horse now.
@arthurdent8086
Жыл бұрын
I always enjoyed the puzzled look on the face of the person I would lend my calculator to, right around the time they started to realize they couldn't find the "=" key!
@erikhicks07
Жыл бұрын
This is 2023. 2+2 no longer equals 4.
@LumbridgeTeleport
4 ай бұрын
Thanks to atheism / secularism
@zirco77
20 күн бұрын
2+2=5 for extremely large values of 2 ;)
@johnburgess2084
Жыл бұрын
In over 73 years in the real world, I've never had a problem like this in actual practice. In Elementary / Middle / High School, tests, etc., the problem might be presented as 6/2(2+1) and I'd just have to do the right thing. But in solving word problems (remember those!) and real-world problems, you (the operator) have inside knowledge of the meaning of the problem you're trying to solve, and you'd just do it right.
@johndorian4078
Жыл бұрын
If i wrote a problem like 6/2(2+1) i'd get scolded for not property writing a non ambiguous equation
@terrytysinger6022
Жыл бұрын
Agree. Never remember this being an issue through university calculus and physics BUT that was just before the computer explosion. Is VERY important now.
@laurencefraser
Жыл бұрын
@@johndorian4078 As I was taught it... we learned order of operations before algibra. Before algibra, you'd probably get told to right the multiplication sign in, and may or may not get an brief aside about how this was short hand that would be learned later on in algibra, but wasn't useful for what was currently being taught, so please don't do it. After algibra was a thing, people would might look at you a little funny, because while 6/x(2+1), or (x/2)(2+1) were generally considered pefectly normal, 6/2(2+1) was something that would generally only come up part way through your working for something that started out more complicated, not as a start or end point. (whether it was an acceptable answer or not would depend on the question... but I'd be hard pressed to think of a situation where a question with that as an Answer would come up (they'd usually want you to resolve the multiplication and division and produce a final result, by the time you got down to something that only had numbers in it like that.)
@QwDragon
Жыл бұрын
When you write it by hand, you'll move text baseline to either ⁶/₃(2-1) = 9 or ⁶/₃₍₂₋₁₎. Nobody writes 6/3(2-1).
@johnburgess2084
Жыл бұрын
@@QwDragon 6÷3(2-1) is exactly the way the problem was presented in the video. Except Dave had the luxury of using a real division sign (the line with dots above and below) which I didn't bother to look up at the time. So I used the '/'. Same problem, same "ambiguity". Nobody writes it as 6÷3(2-1), either, in the real world. Which was my point.
@nezbrun872
Жыл бұрын
I still do use an RPN calculator! But I was a late developer, I made the switch about five years ago. I now find it more difficult to use an infix calculator, because my brain's switched to entering expression as postfix. Two most used are a Swiss Micros DM42 and a WP-34S, but I also regularly use an HP15. Now do a video on the HP16 programmer's calculator, which at one time was a must have especially for the well-healed assembly language programmer.
@ianjlilly
Жыл бұрын
I'm 76 and have been using RPN on HP calculators since the 1970s. I too have trouble evaluating complex expressions without using RPN. First thing I do with each new Android phone is install the RPN calculator.
@michaelclift6849
Жыл бұрын
Me too. Been on the HP48G since ~1995. It also has a clone on the android store. @ianjlilly which android RPN do you use?
@Obscurai
Жыл бұрын
I still have and use my HP 16C.
@fsmoura
Жыл бұрын
After years using RPN every single day, every time I have to use an algebraic mode calculator I trip and stumble like I'm drunk for a few tries. Then I start cursing.
@zapazap
Жыл бұрын
Some would say that you are doing math "wrong" because it is not PEMDOS.
@nujuat
Жыл бұрын
I mean the argument for 1 is an extra unstated rule on top of PEMDAS, that professionals do use, that implicit multiplication takes priority. I think it makes sense and use it. It seems to me like the difference between i and j for the complex unit, it's all the same
@Thirsty_Fox
Жыл бұрын
Correct. Without the explicit multiplication, it's to be treated as if it belongs to the parenthesis, like it was factored out and has to be distributed back in to resolve the parenthesis.
@cassiee.3969
Жыл бұрын
Professional mathematicians *do* prioritize implicit multiplication. Professional software developers don't. Because they don't do the math at all. Instead, they program a computer to do the math for them. And they program that computer... incorrectly.
@okaro6595
Жыл бұрын
@@Thirsty_Fox It just has a higher priority, it does not belong to the parenthesis.
@Zipser2600
Жыл бұрын
Implicit multiplication normally involves multiplying the value outside the bracket to each term inside the brackets 6/2(2+1) => 6/(4+2) Then the brackets 6/(4+2) => 6/6 Then finally the divide 6/6 = 1 The problem is that PEMDAS does not truly handle implicit multiplication/
@Chris-5318
Жыл бұрын
You didn't use PEMDAS. Implicit multiplication has no special meaning using PEMDAS. Why did you evaluate the M before the D when PEMDAS says you should have gone from left to right and so you should have done the D before the M? PEMDAS does handle implicit multiplication, it quite intentionally treats it the same as explicit multiplication. That's because it is trying to be logically consistent.
@noth606
4 ай бұрын
No it doesn't. It means you resolve what is inside the parenthesis down to a single value first before proceeding outside the parenthesis. So hierarchically. 6/2(2+1) becomes 6/(2(2+1)) for process order to 6/(2x3) to 6/6 ending in the same result but different order of operations. At least how it was taught to me.
@NIronwolf
Жыл бұрын
It gives a different answer because it has (as stated in it's manual) a more complex/complete order of operations than just PEMDAS. It has a level between E and M for "implied multiplication". This is also often how scientists write in their papers. Calculator devices still come in both this configuration and the strict PEMDAS configuration today. It's a case of sloppy input from the me problems and inconsistent interpretations of the "right" way to math.
@JJFX-
Жыл бұрын
And now I remember why I always hated math class growing up. Most the time my cynical teachers spent more effort trying to trick us than making sure we understood the subject.
@davidrush4908
Жыл бұрын
Try learning PEMDAS, then moving into engineering calculations where the parentheses bind more tightly to an adjacent number, therefore are not immediately replaced with a multiplication, effectively treating the entire expression as if it were in parentheses. His example of 6÷2(1+2) =9 would instead effectively be calculated as 6÷(2(1+2))=1 Then again, perhaps this is just a logic trap for aspiring engineering students to deal with.
@cericat
Жыл бұрын
@@davidrush4908poor formatting that's designed to spark a war in the comments every time. You get people who are outright wrong, and generally two groups that understand OoO in different ways.
@John-McAfee
Жыл бұрын
The equation is deliberately imprecise to provoke discussion. It's why even well-educated mathematicians are disagreeing, why different calculators and tools produce different results and why there's still no clear answer even though the puzzle has been floating around for years. If you're asked to perform this calculation for anything more important than a Facebook survey, ask where the equation came from and clarify exactly what was intended. Either add parentheses, rearrange the terms, or format it such that all fractions are unambiguous numerator-over-denominator fractions. It is 1 or 9 based off interpretation.
@Thirsty_Fox
Жыл бұрын
Which is what MATLAB makes you do since it recognizes the ambiguity and high chance of error in assuming one way or the other. I'm inclined to say it's 1 based on the knowledge of implicit multiplication (distribution rule) making it part of resolving the brackets, which is the norm in engineering equations, but I recognize that it's ambiguous and others, especially those who maybe don't work with as involved math, will evaluate it to 9. But it isn't how we do math on paper and when I enter it into computers/calculators I enter it unambiguously.
@John-McAfee
Жыл бұрын
@@Thirsty_Fox Yeah, lol the fact he says the answer is 9 kind of pissed me off. There is not a universally recognized convention for evaluating this expression with the formatting provided. 6/2(2 + 1) = 6/[2(2 + 1)] = 1 is juxtaposed [and implicit]. 6/2 (2 + 1) = (6/2) (2 + 1) = 9 is implicit but not juxtaposed. 6/2 × (2 + 1) = (6/2) (2 + 1) = 9 is explicit multiplication.
@ChrisLee-yr7tz
Жыл бұрын
You're just going over the same old ground that's been done a million times. PEMDAS is taught before algebra and is just a tool used by teachers to help young children. Once you've moved on to learning algebra, multiplication by juxtaposition takes a higher precedence. There is no authority that says that PEMDAS is the overarching rule and you're just plain wrong. Although the problem is badly written, anyone using parentheses and dropping the x operator knows that multiplication by juxtaposition should be processed first. There's no other logical way to try and interpret what the problem really means.
@lajosgathy5156
5 ай бұрын
Actually, if you ask a Maths PhD they might say 1 is actually the right answer. If you were to put the explicit * between 2 and ( then it's really 9. Because 2(2+1) actually implies implicit parentheses, so: (2*(2+1))
@wikdipr2944
Жыл бұрын
Part of the problem with the viral problems is that there are multiple conventions in mathematics. In some systems the number next to parenthesis has higher precedence than a multiplication or division symbol.
@addmix
Жыл бұрын
That was my thought. I remember being taught in math that when you have an expression like 2(3+1), the "2*" part is actually part of the equation in the parentheses.
@prose1733
Жыл бұрын
Anything that is outside a parentheses without any operator means it is factored out of the parentheses and the terms inside of it. So yes. Constants, values and variables outside the parentheses, regardless if it's in front of or after, belongs to the parentheses and is not dependant on PEMDAS or any other silly rule. It is ALWAYS multiplied into the parentheses first, or atleast at uni.
@idontknowanygoodnames1498
Жыл бұрын
I think either way of solving the equation is right, as it is written very poorly. This is the reason we don't use the division sign for division. It's too ambiguous, and i think many in the field of mathematics would agree that a number next to a bracket implies a stronger connection then just multiplying, in which case it would be 6 over 2(2+1), which is how it should be written. Anyway i think that's why modern calculators have shifted to using x/y instead of x%y (% was the best i have for a division sign). If anyone wants to argue otherwise, i'm all ears and want to hear your opinions.
@raphaelfranzen9623
Жыл бұрын
The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. Edit:Reply from ChatGPT I understand your point. Juxtaposition is indeed a concept where multiplication is implied when two values or terms are placed next to each other without any explicit operator. However, it's important to note that the use of juxtaposition for multiplication is not always universally accepted, and its interpretation can lead to ambiguity in certain cases. In the case of the expression 6/2(1+2), the ambiguity arises due to the juxtaposition of 2 and (1+2), and this is precisely why parentheses and standard order of operations are used to avoid confusion. Different people might interpret this expression differently, which is why it's a good practice to use parentheses to clearly indicate the intended grouping and operation. If you want to avoid ambiguity and clearly express your intended meaning, it's advisable to use parentheses explicitly, especially when juxtaposition could lead to confusion.
@Chris_5318
Жыл бұрын
That has been coined as PEJMDAS to imply that juxtaposition (AKA implicit multiplication) has a higher precedence that explicit MD. Calculators use either PEMDAS or PEJMDAS, mainly dependent on the region that they are intended to be sold in. ChatGPT mentioned "standard" order of operations. I'm pretty sure that there is no such thing.
@Chris_5318
Жыл бұрын
@inutamer365 No they don't (and you made that first statistic up). Your use of "coefficients" smacks of weasel wording too. Most Americans agree with Dave. Most sources suggest that PEMDAS, not PEJMDAS is THE standard order of ops. Nowhere does PEMDAS say that multiplication by juxtaposition (multiplication) has an elevated precedence. It beats me that anybody ever thought that it was part of PEMDAS. Before you assume otherwise, I prefer PEJMDAS, but I always add extra parenthesis (I call them "safety brackets") so I am independent of the difference.
@Lee.S321
Жыл бұрын
@@Chris_5318 @inutamer365 is correct in that basically anyone who's studied higher education mathematics, such as mathematicians & physicists, just naturally employ juxtaposition (all literature is written that way too), because otherwise complex expressions may become a nightmare to interpret &/or evaluate. The order of operations we learn when we're 10 are simplistic tools to help us learn basic math, which are subsequently abandoned when we take higher level mathematics, because they're no longer relevant.
@northgrave
Жыл бұрын
@inutamer365 Another example without juxtaposition would that 10n/10n = n^2
@Chris_5318
Жыл бұрын
@inutamer365 FYI Mathematica (MM) only uses PEMDAS, not PEJMDAS. Wolfamalpha (WA) uses either, depending on the input given. "2 / 4 x" and "2 / 4 (x)" both gave the result x -- 2 on both MM and WA. Both "a / b c" and "a / b (c)" gave the result a c ----- b on MM WA gave a c ----- b and a ------ b(c) Both gave 9 as the result for "6 / 2 (2 + 1)"
@yamspaine
3 ай бұрын
I intuitively expect the first 2 to be grouped with the parenthesis group If we ever see this, it is a syntax error, it is ambiguous because we don't know what the author was intending.
@darylcheshire1618
3 ай бұрын
I remember BODMAS.
@Luk4sWorld
Жыл бұрын
I own three Casio calculators (fx82, fx991ES, fx991DEX), (40, 10, 5 years old respectively) the two older ones outputs 9 for both "6÷2x(2+1)" and "6÷2(2+1)", the newer one outputs 9 for the first expression as well, but for the second one its 1, and my input got forcibly changed to "6÷(2(2+1))". Thank you for mentioning the change in math rules as even I was under the impression that a implecit multiplication also implicates brackets around it. It never got directly shown or even mentioned during my algebra classes in school.
@4055178
7 ай бұрын
If you are asked to calculate the curve of a thrown ball in a medium you need to use the formula which includes the medium. The result from the simplified formula in a vacuum would be wrong. If you are asked to evaluate an equation which uses implied multiplication you need to use a rule-set which includes implied multiplication. PEMDAS doesn't and gives the wrong answer. Easily seen by the fact that calculators using PEMDAS either make you or automatically insert an explicit multiplication sign. But 6/2(2+1) =/= 6/2*(2+1). The calculators just interprete implied multiplication as if it were explicit multiplication, changing the question. Correctly translating the question to a system without implied multiplication results in 6/(2*(2+1)). With implied multiplication it will evaluate as 6/2(2+1) = 6/(4+2). A scientific law always has to describe reality: Is there a medium or are we in a vacuum? The reality is that implied multiplication is used in the question. PEMDAS is a simplification which fails to describe this reality. PEJMDAS better describes the reality of how this equation will be evaluated.
@carultch
4 ай бұрын
There is a medium, it's just insignificant for the simple situations. It also turns algebra into differential equations, when it comes to solving projectile motion. It's not necessarily wrong to ignore air drag, it's just a simplification.
@sethdesilva
Жыл бұрын
I disagree. Concatenation, at least to me, takes precedent over the division before the 2. Consider the problem: ' 6 ÷ 2x '. I believe most people would agree that the expression simplifies to '3÷x'. Very few would simplify down to '3x'. Let us now consider the problem ' 6÷2(x) '. Are you claiming that the result should now be '3x'? All I've done is factor the two out of the term. Concatenation has higher precedent than simple multiplication and division. With the interest of keeping consistency, I propose either: a) do away with the confusion by disallowing 'concatenation'. b) keep the consistency. '2x' should always be equal to '2(x)' in an expression, irrespective of its surroundings. I'd be interested to hear other peoples' input.
@actually_it_is_rocket_science
Жыл бұрын
For me it comes down to. We don't need to add implicit multiplication or multiplication by juxtaposition. We have all the tools with parentheses to show priority of multiplication if needed. Adding multiplication by juxtaposition complicates math in a similar way to the way English complicates language with rules that only apply in certain situations.
@nilfox921
Жыл бұрын
Concatenation always assumes a * operator between elements. 2x will always be 2 * x, its just to save ink and paper space / disk storage. Remember that the ÷ is really just multiplying the reciprocal of the value right in front of it.
@JouvaMoufette
Жыл бұрын
That's because that's a unknown. You don't know the value so you can't reduce it. You can still reduce it to 3x though and that would actually be the correct answer to reduce it. PEMDAS says Multiplication and Division, left to right, then Addition and Subtraction, left to right. Not multiplication, then division, then addition, and subtraction last.
@diynevala
Жыл бұрын
Totally agree, also let's remove square root (and cubic root) notation and just go with rational exponents.
@sethdesilva
Жыл бұрын
@@actually_it_is_rocket_science absolutely. I prefer parentheses! In this case however, where we're missing some info, I lean toward what I believe more consistent. 2x and 2(x) in my mind should be the same. Thanks for your response though :)
@Just_Klaas
7 ай бұрын
Years ago, I had a discussion with my father, who did not understand the following sum: ½:½=1. If I put it like that, it makes sense. But when I told him it sounded to him like half divided by half and that is ¼. His argument was that if you have half an apple, and you divide it in half, you have a ¼ apple. No matter how I explained it, he never understood and believes it.
@GanonTEK
6 ай бұрын
I think it's the subtlety in the difference language-wise even that can cause confusion. ½ divided by ½ is indeed 1 but your father likely interpreted it as ½ of a ½ which is ¼ or maybe as ½ divided in ½, which is (½)/2 = ¼ also. or as ½ divided by 2, which is ¼ also. My guess is he interpreted it as ½ divided in ½ (which is ¼) instead of ½ divided into ½ (which is 1) A small change, into and in, makes a big difference.
@davidt9902
Жыл бұрын
y = mx + c has an implicit multiplication between the m and x 2ab ÷ 2a ≠ 2ab ÷ 2 x a as b = a²b only if b is zero or a = ±1 for real values of a and b Replacing an implicit multiplication with an explicit multiplication to reason about the precedence does not demonstrate anything about the precedence of implicit multiplication vs division.
@101perspective
Жыл бұрын
In 1982 I saved up and bought a trs-80 pocket computer. That thing was awesome at school. Computers were still new enough that teachers had no clue that a pocket computer even existed, let alone the power of it. They just figured it was a fancy calculator. Which it was. However, you could also program it to do all kinds of things. Like not only calculate complex problems but to also show you each step in getting to the final answer... in case you needed to "show your work"...lol. I personally seen no problem with using it in this way since I had to have a complex understanding of how to do the problem in order to program the computer to do it for me. All the program did was speed up the process significantly. Which was especially helpful for homework since I held 2 part time jobs during HS.
@steveo104
Жыл бұрын
That’s awesome! Knowing how to do the problem is one thing. Knowing how to program a computer to do the problem and output steps should just be an automatic A.
@BigMikeECV
Жыл бұрын
I did something similar with a programmable TI calculator during tests in my calculus class in the early '80s. I could enter an integral into the thing and it would approximate the solution using Simpson's rule. While it spent minutes calculating, I would solve the integral, and then compare my precise answer against the approximation returned by the calculator. If they were very close, I knew I had solved it correctly.
@LeeMyers-Jr
Жыл бұрын
In college I bought me a HP48 calculator, I was a Physics Major with a math minor. The nice thing about the HP48 is you could program it. But since I didn't do any repetitive calculations, it was easier to do it by hand rather than program the calculator. I did program one thing on it. I programmed a stopwatch on it. I was a Cub Scout leader and needed a stopwatch for an activity, didn't have a stopwatch so I programmed a $400 calculator to be the stopwatch.
@hughobyrne2588
Жыл бұрын
The KZitem channel, "The How and Why of Mathematics", has, IMHO, the best videos (2 of 'em) on how this expression works, and should work. She brings the receipts, too, with real examples of expressions from math and physics textbooks.
@PattyManatty
Жыл бұрын
She is the only video I've seen on this topic with a good take. Find me any mathematical paper that interprets 1/2x as one half x....
@ska4dragons
Жыл бұрын
The problem is it is very difficult create a new rule for something like math. At best you will create a "regional difference" within mathematicians. So she brought up a few examples of the usage of juxtaposition priority. Just because something is done does not mean it should be done. If there is ambiguity there are 3 solution. 1. Avoid or explicitly prevent the ambiguous notation. 2. Go with the interpretation that is most consistent with existing rules without the need for providing new information to users/interpreters. 3. Create a new rule that enforces the interpretation you prefer. These are orded by effectiveness. They are also ordered by the usage we see in the real world. Almost all software uses #1. Division bar is usually forced so divisors are directly under the bar. Mathematicians almost always agree that ambiguous notation should not be used. #2 is usually used instead. Not by people writing notation but by interpreters. You can see many examples of this in this very video. Almost exclusively calculators and other interpreters use order of operations we learned in school and not priority for juxtaposition. I only know of like1 or 2 examples of calculators using juxtaposition priority. Juxtaposition priority is new info that needs to be passed on. It is a rule that needs to be implement/enforced. #3 is the least effective because it requires getting information to all the people affected by the change and enforcing it. No matter how many anecdotes you can cite of usage, you can't say this is the *right* way or we wouldn't have dozens of examples of this going viral. It's viral because it's controversial. It isn't controversial because people are uninformed either. People of all sorts of math backgrounds can be on either side.
@MadocComadrin
Жыл бұрын
@@ska4dragons You have it backwards: juxtaposition is not "new information" and was given precedence consistently before PEMDAS was invented (by teachers, not mathematicians). And indeed, PEMDAS created a "regional difference," not only geographically (where both educators, laypeople, and professionals in many countries say that juxtaposition comes first), but also between laypeople and mathematicians/scientist who give juxtaposition precedence. "Mathematicians almost always agree that ambiguous notation should not be used" - not being ambiguous often relies on agreeing on precedence, otherwise (1 + 2 * 5) would be considered ambiguous too. Juxtaposition is not ambiguous (in terms of precedence) when the precedence rule exists, and the rule that has the most common usage in mathematically relevant circles has been and still is giving juxtaposition higher precedence. You can check the videos on the channel mentioned in the top-level comment for proof. "Almost all software uses #1": almost all software doesn't allow juxtaposition in the first place. Allowing juxtaposition in expressions makes designing a formal grammar (and therefore a parser) somewhat more difficult.
@billv4987
Жыл бұрын
(1/2)x is one-half x. 1/2x is a stupid linkedin "discussion" with 5,000+ answers.
@ska4dragons
Жыл бұрын
@@billv4987 Division is not commutative. You cannot freely move the divisor in an expression similar to multiplication. So, I'd argue 1/2a is always implied to be (1/2)a
@markrosenthal9108
4 ай бұрын
PEMDAS is merely a convention. A mathematical notation's purpose is to simplify comprehension. Ken Iverson recognized that PEMDAS fails at this because of the non-intuitive special cases required to make it work as demonstrated in this video. With Iverson's computational notation described in the book 'A Programming Language' published in 1962, he used simple right-to-left evaluation with optional parentheses (fewer than required by PEMDAS) when needed to improve clarity. In APL: 6÷2×(2+1) 1 So, the correct answer is 1 unless you are using PEMDAS. If you wanted the expression to yield 9, in APL it would be: (6÷2)×2+1 9 Common grammar school symbols for multiplication and division also improve comprehension. And of course, not only engineers loved RPN calculators. I had a spreadsheet application running on an HP3000 that used RPN instead of infix for formulas.
@pDaleC
Жыл бұрын
I'm extremely pleased that on the HP Prime (in algebraic mode), this expression is a syntax error, and in RPN mode it's a constant function (6/2) applied to another constant (1+2) and the value is 3! (The calculator DOES warn you.)
@adamsmall5598
Жыл бұрын
The value is 3factorial?
@blacktomb7264
Жыл бұрын
Last example is basically how i always think about these, because here you know that dividing by 2 is the same as multiplying by 1/2 (and there is nothing that tells you the parenthesis is inside the division) so you end up having three multiplications in a row, which makes it easier to understand when solving left to right.
@banggugyangu
Жыл бұрын
In single line notation, if multiplication is used without a sign, then it is the relation of a coefficient and not just simply multiplication. Coefficient relationships cannot be separated without equivalence.
@TheObsesedAnimeFreaks
Жыл бұрын
f(x) is what those parenthesies are, so you HAVE to clear the f(x) first.
@RexxSchneider
Жыл бұрын
So 1/2x is exactly the same as x/2, right? So why do bother ever writing 1/2x? Why should we have to add unnecessary parentheses to write the reciprocal of 2x?
@samd2660
Жыл бұрын
6 /(4x+2) where x = 1 is 1, if you do the maths that equation is (funnily enough) is equal to 6/2(2x+1), which you're saying is now equal to 9
@JesuszillaS
4 ай бұрын
My calculator I’ve had since high school, the HP-33S is an RPN calculator and I still love it even as a computer scientist! My chemistry teacher recommended it back in high school and said once you got used to it, you wouldn’t want to use any other calculator and he was kinda right
@timberwoof
4 ай бұрын
It annoys me that the "RPN" calculator on MacOS handles the stack wrong. I should write a correct one that takes key inputs.
@AllanKobelansky
4 ай бұрын
I was using an HP25C in 1978. Then went on to use an HP67 (with the mag stripe reader) then the HP41C. RPN makes these equations trivial.
@bruceblake530
Жыл бұрын
There is a mathematical expiation for for the answer 1 it is monomial numbers. When a number is written without the infix sign such as 2y it is a monomial and so should be interpreted as (2*y) not as 2*y. You can verify this by the monomial and polynomial therms.
@hansangb
Жыл бұрын
Proud owner of HP-41CV. It had linear algebra and circuit analysis pacs so it was pretty much mandatory. And once you learn RPN, there's no going back. Also, I remember a rule about proximity (?) , that would mean 1 is the correct answer.
@billj5645
Жыл бұрын
Agree- I bought an original HP35 when I was in college and have used RPN since. That calculator didn't even have a model number on it. I assume when they made it they didn't know if it would be successful or if they would every make another model. Later when they came out with the HP45 they started putting a model number on the HP35. Search pictures and you should be able to find them with and without the model number. I also have a 41C.
@TevelDrinkwater
Жыл бұрын
Have an HP 35s and an HP 50. Apparently the last of HP's RPN calculators. Of course I use the calculator on my phone most now, which is why I use RealCalc, which supports RPN.
@hansangb
Жыл бұрын
@@TevelDrinkwater Yeah, RealCalc is awesome. My every day is 32, but have the 12 and 35 in case my 32 dies one day! Between the three, hopefully I'm set for life LOL. Also, how many RPN users had the "hey, can I borrow your calculator?" "Yes, but...ahhhhh it's RPN sooooo" "Whatever, let me use it....HEY! where's the EQUAL sign???"
@aaronbredon2948
Жыл бұрын
I have a 41CV too. My father passed his HP35 on to me when I was in High School. It got a lot of use. Understanding RPN and how to translate algebraic notation into postfix helps one learn to avoid ambiguity. The HP12c RPN calculator is still sold by HP. And HP now has some graphing caculators that are RPN.
@aaronbredon2948
Жыл бұрын
@@linusfu515 if the equation were: N=1+2 ; 6/2n Then you would be correct, but the implied association only applies for algebraic variable letters and symbolic constants like π. When the only thing being is a parenthesized expression containing numbers only, that does npt apply. 6/2(1x+2x) is 6/(2×(1x+2x)) by default because it is algebraic expression with a variable and requiring parentheses every time you have 1/2x complicates things. But 6/2(1+2) is (6/2)×(1+2) by default because it is an arithmetic expression. However, in both cases, there is ambiguity that should be resolved with proper parentheses. If the problem just says to provide the answer to 6/2(1+2), the question is about grade school arithmetic (even if the problem is in a higher math class), and the answer is unambiguously 9, since there is no precedence level in PEMDAS/BODMAS for implied multiplication. If a grade school teacher is teaching that implied multiplication has a higher priority than regular multiplication/division, then that teacher is teaching incorrectly. If there is more to the problem, and 6/2(1+2) is only part of the presentation, the context should indicate the official meaning, and a comment should be included in the answer that the formula as written is ambiguous. If 6/2(1+2) is part of the answer you write, expect to have points taken off for not writing it in 2 dimensions and using a vinculum and/or not parenthesizing properly.
@paul_om4822
Жыл бұрын
Gawd damn, I picked up degrees in maths and engineering 40 years ago and I still think the answers 1. Looks like I might have to learn something new today ;-/ thanks Dave
@nixboox
Жыл бұрын
It is one. Because every person who does these videos fails to do the distributive property. The parenthesis has to be evaluated WITH the distribution of the thing attached to it. If you write the expression as a fraction it becomes obvious that everyone is doing it wrong.
@nagyandras8857
Жыл бұрын
Don't worry , 1 is the correct answer. Implicit multiplication is not something calculators usually understand.
@mufaro_xyz
Жыл бұрын
@@nixboox No, it's not. Maybe if you're from USA the lack of good education didn't teach you that one correctly but you're forgetting how brackets work and when left to right notation is applied.
@hughobyrne2588
Жыл бұрын
You want to learn about order-of-operations, really the best resource in KZitem is two videos by the channel "The How and Why of Mathematics". I forget the exact titles, but you'll recognize them when you see them.
@ZelphTheWebmancer
Жыл бұрын
@@mufaro_xyz Left to right is not a thing. The correct answer is 1 because juxtaposition, or implied multiplication. When you have 6/2(1+2) after solving the parenthesis (which are always done first) you go for the juxtaposition and get 6/6 which is 1. Left to right just happens to be a right sometimes as a coincidence, I never saw that in my school years and I'm from Brazil.
@VieShaphiel
Жыл бұрын
It's been decades since I actually used that division sign that I was actually confused for a moment.
@bluephreakr
Жыл бұрын
Most open-source distributions providing X window server are pretty rad for the compose function. IN the absence of a dead key to enable (⋄), most desktops provide an alternate button to press which overrides normal keyboard use while in effect. Short of that, Windows users can use WinCompose to emulate this with macro inputs. ⋄:- = ÷, ⋄xx = ×, ⋄ = ⋄ etc.
@fsmoura
Жыл бұрын
Wow! How did you even survive!? Are you just going through life winging it blindly like a bat?? ( o.o)
@VieShaphiel
Жыл бұрын
@@fsmoura No I mean I always use /, so I was like "does ÷ have a different rule or not?" (which is still silly, i know)
@fsmoura
Жыл бұрын
@@VieShaphiel Ah, of course! Phew, I was worried for a moment (" o.o)
@lyrimetacurl0
Жыл бұрын
2÷3÷4 feels like it goes left to right and 2/3/4 feels like it goes right to left. Same as 2^3^4 famously goes right to left also, and that's not what PEMDAS says either.
@KLR-3
22 күн бұрын
PEMDAS is supposed to solve this ambiguity but clearly we don't even agree on the rules of PEMDAS. I suppose it would help to know where it is explicitly defined. I've never heard the rule that you should drop the parenthesis and reduce it to a simple multiplication sign. I think that step changes the problem and removes the precedence of the parenthesis. Furthermore, it would contradict the distributive property. 2(2+1) becomes (4+2) then (6) leaving the overall problem to be 6/6 which = 1. Given the distributive property, I would conclude that the correct understanding of PEMDAS is that the parenthesis applies to a term not separated from it by another operator. (Which is how I was taught in school.)
@fozzzyyy
Жыл бұрын
Implicit multiplication ranks higher than explicit. Is 1/2x equal to (1/2)x, or 1/(2x)? I think most sensible people would say the second, because if you didn't mean that you would've just written x/2 instead.
@tammymakesthings
Жыл бұрын
Order of operations and the PEMDAS rule would say that 1/2x is equal to (1/2)x because multiplication and division are applied from left to right. Trying to be clear about what you intended would argue that you should avoid implicit multiplication. But as Dave points out, the fact that implicit multiplication is unclear doesn’t change the operator precedence rules.
@jamescollier3
Жыл бұрын
yes. PEDMAS HS. Implicit multiplication college level. MS and calculator primary customers: The Schools. follow the money lol.
@mustangccx66
Жыл бұрын
f(x) = 2*x, f(x) at denominator 1/f(x) ⇔ 1/(2*x) 1/2x is common spelling mistakes
@tomtrombley2402
Жыл бұрын
6/2(2+1). Consider this: how do I factor (4+2)? I can take a 2 out of each term, which I would rewrite like this: 2(2+1). In this case 2(2+1) is a term that must ALL be factored together, in which case 6 would be divided by 6, and the answer would be 1. It is a “not enough information” assumption to assume that the 2(2+1) is NOT a single term, which MUST be assumed for the answer to be 9. The reason for not enough information is a lack of a standardizing rule that makes one or the other solution no longer possible. I believe that the example I have given demonstrates why the rule should be that considering a lack of an explicit multiply symbol considers all conjoined characters as a single term should be the rule of the day OR that parenthesis should always be enforced such as 6/(2(2+1)), though the latter still leaves some logical problems to be solved. Logically, given the limitations introduced by the ambiguity of the rules at the moment, the answer is either 1 or 9.
@Hackybaby
5 ай бұрын
Thank you, thats exactly my thought.
@Fishezzz
4 ай бұрын
6/2(2+1) can also be written as 6*½*(2+1) so your factoring is wrong. It would be factored as (1 + ½) which is ³/². So that would be 6 * ³/² which is also 9.
@keensoundguy6637
4 ай бұрын
«It is a “not enough information” assumption to assume that the 2(2+1) is NOT a single term» If you want it to be a single term, then you must "spell" the expression differently. If you think there's "not enough information" then you missed out on some fundamentals during your education. So the real problem when encountering expressions like this one is that you have to wonder if the person who wrote it is someone who thinks as you do.
@LuaanTi
4 ай бұрын
There is no special rule for multiplication by juxtaposition. It's multiplication like any other, and has the same priority as division, so you have to evaluate left to right. Just because the multiplication symbol isn't written out explicitly doesn't change anything about the order of operations. Don't use the division sign. It's eeeevil :D
@swartley
4 ай бұрын
Unless i completely misunderstood my teacher, a parenthetical without a multiplication sign was an implied extra parenthetical. Super fun unlearning things 2 decades later.
@YEC999
4 ай бұрын
I would actually see it like your teacher. A casio fx-82MS which was/is? for decades a school math calculator does it that way. Most people feel that multiplication by juxtaposition is of higher order. Most people that write it that way. PEMDAS actually letter by letter states that multiplication comes before Division. What does the other side have? An arbitrarily used PEMDAS for children. Why shouldn't multiplication by juxtaposition be of higher order? What is the argument for that?
@LuaanTi
4 ай бұрын
@@YEC999 The real problem is the division sign. In actual mathematical notation, you rarely see it at all, you'd just use a fraction. PEMDAS is, like many teaching tools, misleading. Addition and subtraction have equal priority, and multiplication and division also have equal priority. Surely you wouldn't say "3 - 2 + 1" equals zero, would you? Addition doesn't have priority over subtraction and neither does multiplication over division. Don't use the division operator. It sucks. When you have to, use parentheses. People will _always_ be confused about the intention of that expression, regardless of whether they know the proper operator precedence or not, because they always have to think about all the other people who potentially _don't_ . If you write an expression like "6/2(2+1)" you deserve to be dipped in tar and rolled in feathers :D
@FunkyMooch
4 ай бұрын
That's called multiplication by juxtaposition... which is part of algebraic expressions. Like, when you go from 3y+2x+2 you can rearrange the expression as 3y + 2(x+1)... This also applies to multiplication and division... 3y / (2x + 2) = 3y / 2(x+1). The problem is syntax, does 3y / 2(x+1) mean 3y divided by 2(x+1) or does it mean 3y/2 multiplied by (x + 1). This nuanced difference gets to mean something in more complex expressions. Usually in more complex expressions, the numerator and the denominator are expressed explicitly to avoid confusion. The multiplication by juxtaposition should be specified in the users manual.
@TomNimitz
4 ай бұрын
I always wondered about the quadratic formula - since PEMDAS does not include juxtaposition, over/under fraction notation, or root (and many other notations not taught before middle school), it seems that those notations should be ignored and the closest PEMDAS approximation inserted in their place. Now I know you calculate 𝗯² - 𝟰 × 𝗮 × 𝗰, take its root (even though not covered by PEMDAS), divide that root by 𝟮, multiply by 𝗮 and only then add or subtract all that that from -𝗯. In other words, the PEMDAS interpretation would be -𝗯 ± √(𝗯² - 𝟰 × 𝗮 × 𝗰) ÷ 𝟮 × 𝗮. Or perhaps you could say that if a formula contains notations beyond 5th grade arithmetic, you need to look beyond PEMDAS to understand the proper interpretation. Bottom line: If you are in 6th grade, you want to follow PEMDAS to conform to the simplified view. But if you are in the real world you need to recognize that juxtaposition customarily has a higher precedence in engineering, physics, and other fields involving higher mathematical. Time to drop the training wheels and set PEMDAS aside.
@GanonTEK
4 ай бұрын
Just some small points. Yes, PEMDAS doesn't contain implicit notation (multiplication or otherwise, like how Sin²x means (Sin x)²). No, PEMDAS does take roots into account since roots are a form of Exponents. They are fraction powers, so are part of the E step. If you have a two line fraction, that could be interpreted to represent division, which is in the order of operations, where the expression doing the dividing must be placed in brackets. It's best to resolve the top and bottom separately and after that look at the fraction as a whole for any final bit of simplifying. a -- b is always (a)/(b) regardless of what "a" and "b" are. In that simplest case, the brackets are not necessary but in a more complex one they are. If "a" = t²-1 and "b" = t+1 for example. PEMDAS should only have an issue with the ÷2a part in the quadratic formula.
@Tabu11211
Жыл бұрын
I busted out laughing so hard at that rewatch at 75% joke!!
@wictimovgovonca320
Жыл бұрын
I wonder how many people didn't get the joke until they did the 75% rewatch.
@rh4009
Жыл бұрын
What is the name he mentions as the original author of that joke? "Gerald Vandan" is what I head, but can't find google references to this person.
@davestorm6718
Жыл бұрын
Following the rules we were given in college, the correct answer is, indeed, 1 The reason why is you solve the parenthetical first, solve the parenthetical a SECOND time. The part 2( is part of the parenthetical area. Any number that is adjacent to a parenthesis is part of the parenthetical. This is in Principia Mathematica. Don't take my word for it, the second term when expressed b(c+d) expands to (bc+bd). You expand until all parenthetical multipliers are removed, then the EMDAS is left over. So for a÷b(c+d) , expanding the parenthetical term, becomes a÷(bc+bd) . It's still a parenthetical, so solve inside the parentheses first again following orders of operation, and you get 6÷(4+2) => 6÷(6) => 6÷6 = 1
@eazegpi
Жыл бұрын
This could not be more wrong. Terms outside the parenthesis are not part of the parenthesis for the obvious reason that they are outside it. b(c+d) expands to bc+bd, no parenthesis.
@ska4dragons
Жыл бұрын
You were taught wrong.
@eazegpi
Жыл бұрын
@@ska4dragons Dude, Dave just showed like 10 resources that explain step by step how you are wrong and you think I was taught wrong?? Your cognitive dissonance is astounding.
@ska4dragons
Жыл бұрын
@@eazegpi Dude, who's talking to you?
@eazegpi
Жыл бұрын
@@ska4dragons damn, I'm a moron. I thought you were the first guy. I'm sorry.
@bxdanny
Жыл бұрын
I think the use of the expression "2(2+1)" (without an explicit operator after the first 2) could be taken to make the larger expression mean 6÷(2*(2+1)), which really is 1. Of course, you can't enter it into a calculator that way (with no explicit operator).
@adrianedge854
Жыл бұрын
Yes the implied multiplication is the main issue. And that was surreptitiously avoided through the inability to enter that in to many of the examples
@wodmarach
Жыл бұрын
Suprisingly on non-US made calculators you generally CAN assume they'll handle Juxtapositions correctly as far as I know only TI and HP calculators don't work this way and even then some of theirs do actually understand juxtapositions you literally have to check the manual to be sure if they do or not each time you get one >.
@bluedark7724
Жыл бұрын
Order of Operations = correct result
@wodmarach
Жыл бұрын
@@bluedark7724 only if you know the actual order and don't rely on PEDMAS as your order
@dino6627
Жыл бұрын
I agree 6/2(2+1)=1 which is not the same as to 6/2*(2+1). Implicit multiplication, has priority over division, the 2(2+1) is evaluated first. This has been standard practice in mathematics and engineering for decades. Adding an explicit multiplication symbol, changes the expression, the priority and the result to 9.
@user-tg2gm1ih9g
3 ай бұрын
arithmetic in English does not have precise precedence rules ... so use parentheses to clarify (6/2)*(2+1) = 3*3 = 9 OR 6/(2*(2+1)) = 6/(2*3) = 6/6 = 1 or we all could adopt the precedence rules of APL (a programming language, Kenneth E Iverson, 1962) and process all operations (strictly) right to left. 6÷2*2+1 = 6÷2*3 = 6÷6 = 1 ☺
@Pablonmon
Жыл бұрын
I had always used the term 'reverse polish notation' for the postfix representation. It was never the topic of discussion when I worked with other engineers, so hearing it hear was both informative, and a nice blast of nostalgia. I recall deriving the same tree structure to implement RPN for a class assignment.
@DavidTaylor-es1bt
Жыл бұрын
I always heard "reverse polish logic" as the term used by engineers and scientists. This is the first time I heard "postfix".
@theantipope4354
Жыл бұрын
Yes. 'RPN' (Reverse Polish Notation) is what HP calls it too.
@tedlassagne8785
Жыл бұрын
Now, class, can anyone tell me why it's "reverse" and why it's "Polish"?
@Acorn_Anomaly
Жыл бұрын
@@tedlassagne8785 Yup. (And this is all info I already new, but I did have to look up to confirm the guy's name.) It started with what we can call prefix notation, invented by Jan Łukasiewicz. It was called "Łukasiewicz notation", and then, because people were lazy and couldn't remember how to properly spell his name, "Polish notation"(since he was Polish). Polish notation had the same advantages that postfix notation does - it's unambiguous. The only difference is that, when writing Polish notation, the operator comes before the operands, not after. So, for example, 5 * 3 + 2 could be written as + * 5 3 2. Postfix notation is the complete reverse - reverse Polish notation. (The same formula above would be written 2 3 5 * + in RPN.)
@hansangb
Жыл бұрын
@@Acorn_Anomaly interesting. I knew the Polish part, but never did understand where the Reverse came from. Thanks
@ame7165
Жыл бұрын
i agree with you on nearly everything dave, but this one i do not. if we go by the slightly ambiguous PEMDAS, sure. but PEMDAS is not correct and most people in the engineering fields agree that you should perform juxtaposition before division and multiplication. PEJMDAS is better
@FloydMaxwell
Жыл бұрын
I had the SAME Sharp calculator back in my engineering days. Could store 49 commands and had PB (playback) so you could check/edit long formulas. Awesome calculator. There is a way to drain your Sharp calculator's battery....quickly. Give it a long equation composed of a lot of very large calculations. I forget what the max factorial was on the calculator. Say it was 47! So the equation would be 47!/47!*47!/47!*47!/47!*47!/47!*47!/47! etc. until you had used up the 49 commands allowed. Then hit equals. My longest/slowest would take almost a minute. Since the calculator retains the last mighty equation, you can hit equals again. etc. All I know is I changed my batteries at least once in the three years I had the calculator. I bought the Sharp instead of an HP RPN calculator because of the guy in the UBC bookstore. He said, simply, "This is what the Chinese are buying". I'm eternally grateful that I never had to suffer with an RPN calculator.
@SuperS05
14 күн бұрын
That old rule was still being taught in places. My school board did.
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