Very nice explanation! I was able to make the graph, but when it came to plotting the points I got lazy and started looking for an alternative method :P
@quandarkumtanglehairs4743
27 күн бұрын
Haha! Right? I've had to go back, recently, and force myself to do the long way through many different calculations from my youth, finding I'd become lazy, and weak, from dependence on my shortcuts. We need both, both the long-way for detail and thoroughness and reminders of justifications, and also shortcuts for mid-calculation summarizing for handling encapsulated values and relations in a manageable way.
@user-cd9dd1mx4n
27 күн бұрын
Fantastic solution! I really appreciate how systematically you approached the problem, making it easy to follow and understand. Your channel is truly a gem for anyone looking to improve their math skills, and your way makes learning enjoyable. Please keep uploading such excellent videos! Your dedication and clear explanations are incredibly valuable. Apart from the maths, I like your English accent, it is amazing. Like from Saudi Arabia 🇸🇦
@DrBarker
27 күн бұрын
Thank you so much!
@TikeMyson69
27 күн бұрын
Agreed 100%
@decare696
27 күн бұрын
omg! Two of my fav irrational numbers in one video!
@ccrypt949
23 күн бұрын
Great video, will work great with my lower sixth pupils as a bit of a side note to the regular A-Level course
@zathrasyes1287
27 күн бұрын
Thx for another good friday-math.
@brachypelmasmith
27 күн бұрын
can this be solved mathematically, without drawing the functions or is graph required
@anthonyserafini
26 күн бұрын
It can be solved, but is less pretty. You basically have to manipulate inequalities to show that the floor and ceiling will have different values at certain intervals.
@francescocostanzo8225
24 күн бұрын
This is an incredible video. Where do you get your inspiration?
@DrBarker
24 күн бұрын
Thank you! For a video like this one, I usually decide, for example, that I want to solve a weird equation involving the floor function. Then it's a matter of playing with different starting equations, and trying to find a nice method of solving, until I find something that I'm happy to record.
@archangecamilien1879
27 күн бұрын
Interesting question, lol...have to write this algebraically, etc, in equations, but basically you have to make sure that they are within two integers, etc, like if you draw a line at each integers, forming a grid of horizontal lines, you have to make sure they are within two grids, one (x^2 -x or something) above the middle line (so it's floor is on the middle line), the other (1-x^2) below the middle line (so its ceiling is on the middle line), but above the bottom one (so it's ceiling isn't there)...should be easy to write in terms of algebra, but I can't do that in my head, lol, not very good with my head and I'm in a hurry...
@TheLuckySpades
27 күн бұрын
Algebraically you can exclude the outside regions by showing that one side is >=2 while the other is
@archangecamilien1879
26 күн бұрын
Ah, I see...I actually typed a comment some 20 mins after I wrote that with my approach to it, but I don't see it...something about regions where 1< (x²-x) - (1-x²)
@alaricsnellpym
27 күн бұрын
Hmmm, you say "smaller" for "closer to negative infinity"... I try to use larger/smaller for distance or proximity to 0, and higher/lower for the proximity to positive or negative infinity, as I felt that's less confusing. But you're a far better maths educator than me. Am I wrong? Should -1000000 be considered a smaller number than -1? 🤔
@samueldeandrade8535
27 күн бұрын
Man ... don't make up rules. Or if you want to do that, make some good rules.
@F_A_F123
27 күн бұрын
It doesn't really matter
@alaricsnellpym
27 күн бұрын
"Don't make up rules"? "It doesn't really matter"? Have neither of you ever met a typical mathematician before? 🤣
@TheLuckySpades
27 күн бұрын
The relation you describe is different from what is typically meant with
@alaricsnellpym
27 күн бұрын
@@TheLuckySpades I'm treating signed numbers as a vector quantity, with a magnitude and a direction (albeit only in 1d) when I talk about "larger and smaller", I'm comparing magnitudes!
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