It took you around 3 minutes to say what I needed to know, the same thing that my professor unsuccessfully tried to explain in one hour. Thank you so much
@v-neko8074
3 жыл бұрын
same
@tristanfan4741
3 жыл бұрын
so fucking dmn right
@finghinmccarthy5021
2 жыл бұрын
True
@JuuzouRCS
2 жыл бұрын
True. I am right now going through the same experience.
@shreyas_._
2 жыл бұрын
I wonder which professor took one hour for congruence 😅then for sure your whole syllabus time schedule gonna wasted..., ഒരു മയത്തിൽ ഒക്കെ ആവം കേട്ടോ ...
@johnlara1365
5 жыл бұрын
I am a senior math and CS major, I have used modulo almost as much as I’ve used pi and I have always been confused by congruency. No one has been able to explain congruency more clearly and digestible than you. Thank you!
@dominicellis1867
Жыл бұрын
Basically you throw out the quotient and keep the remainder. It's periodic math like the roots of a trig function.
@GraceJoe-u6y
6 ай бұрын
I watch 7 videos of about 20 minutes about modular arithmetic and didn’t understand anything but your 6 minutes video made me understand. I don’t know what to say
@v-neko8074
3 жыл бұрын
Some teachers in universities: 2h lecture blacklenredpen: 6minutes
@davidbrisbane7206
3 жыл бұрын
Too right mate, plus we can repay bprp's videos as often as we like.
@mohammedhussain6749
3 жыл бұрын
He is just explaining the procedure not the theory, origins or proof
@EulerJr_
3 жыл бұрын
@@aymenchamia7470 I do, and he is 100% right. Our lecturer is extremely smart and knowledgeable no doubt, but he just can’t explain the procedures and concepts in a simple enough way for anyone to understand.
@rainyday4709
2 жыл бұрын
30min trying to understand this congruence with my book . And this man make me understand it just in 1:46 seconds I wanna cry . Why professor make life complicated whyyy ... THANK YOU SO MUCH. I really respect you 🙏🙏
@meccamiles7816
5 жыл бұрын
Your ability to change the marker you’re writing with so fast is amazing...
@krimzonghost1987
3 жыл бұрын
I read this comment and watched the video again just because of this. lmao. Wow! You were not joking.
@sergioh5515
6 жыл бұрын
PLEASE MORE MODULAR ARITHMETIC! You're the best
@blackpenredpen
6 жыл бұрын
Sergio H will do!!
@Jack-cm5ch
6 жыл бұрын
Omg saving my grade once again. God bless you. Wish you had a patreon...
@Wannabesage336
5 жыл бұрын
For those of you watching this in the future: He does! www.patreon.com/blackpenredpen
@billofrights5064
6 жыл бұрын
When I took abstract algebra, I found a ≡ b (mod n) quite confusing. The meaning seems to be a (mod n) = b (mod n), but equivalence must mean more than this.
@WSUFan2017
6 жыл бұрын
You should do more number theory, especially stuff like Euler’s totient function (since it’s my favorite subject ;D)!
@blackpenredpen
6 жыл бұрын
I will. In the meantime, you can check out Max's videos here: kzitem.info/rock/P-ZCMz7olJPUI78b_bQrvQvideos?disable_polymer=1
@roof310
Жыл бұрын
(by wikipaedia) Actually, the first claim is the most correct one, same remainder when a and b are divided by n, a = kn + r, b = jn + r then we have a - b = (k-j)n + 0 which means that n | a - b (the last claim). If we add b to both side, a = Kn + b by setting K = k - j. edit: depends on variables to choose the most suitable one.
@nirmaljyotieducationclasse9965
4 ай бұрын
bro you really came through i was having trouble understanding that claim
@yon1623
Жыл бұрын
I spent an hour trying to understand it from my book... 6 minute video is what i needed.
@arnasvaicekauskas7693
6 жыл бұрын
Why is this video 2Pi minutes long ?
@blackpenredpen
6 жыл бұрын
It's Tau
@unoriginalusernameno999
6 жыл бұрын
Burn!
@ansper1905
5 жыл бұрын
2π=6
@sieger358
5 жыл бұрын
@@ansper1905 😑😑😑3.14159265358979323846264338 ... In can not be 3😐
@ansper1905
5 жыл бұрын
@@sieger358 tell that to engineers
@azure3544
5 жыл бұрын
I learned more from this guy than from my entire math class xDDD My math teacher made this look like rocket science...
@reahjanegalangue8343
5 жыл бұрын
same hahahahahahahhaha
@Mindmodic
4 жыл бұрын
Finally I've been looking for a decent explanation for this for about an hour! Years ago when I was in school we never learned this and 'remainder' was only referred to when you were doing sums by hand, the remainder would be the next 10, 100 or 1000 etc. from your addition, I didn't see it as any other sense!
@barence321
2 жыл бұрын
In Beachy 4th Ed., the authors write " a ≡ b (mod n) if and only if n|(a - b)." The proof goes in both directions, so you see that n|(a -b) does indeed show that a/n and b/n have the same remainder. I just finished going over this proof again for my abstract algebra class. Very simple when you do the proof both ways.
@GreeeenT
6 жыл бұрын
do you have my schedule or something ?? how do you always upload what I need. thanks man !
@blackpenredpen
6 жыл бұрын
OH wow!! ; )
@krimzonghost1987
3 жыл бұрын
C# exercises led me here... and I ain't even mad. Awesome video!
@juandelacruz9125
6 жыл бұрын
Thanks blackpenredpen for teaching us this!
@shady153
Жыл бұрын
This video was awesome! I'm so glad I found your channel. You have a new subscriber here.
@nithin8432
2 жыл бұрын
just had a great and clear understanding this was the lecture i needed thanks a lot mate!!!
@vegetaiv9275
11 ай бұрын
Your explanation is amazing. It is way better than my professor's! Thank you so much!
@UnathiGX
6 жыл бұрын
This is by far the best explanation....IMO!...here I come....!!!!
@blackpenredpen
6 жыл бұрын
thanks!
@jihyepark9139
5 жыл бұрын
Our major instructor discussed this topic like using speed of light.... Boom finish!!
@reahjanegalangue8343
5 жыл бұрын
our instructor doesnt discuss to us hahahahahaha boom
@zellpeppers8181
Жыл бұрын
thankyou so much!! this really helped a lot 🥰🥰
@jgz919
Жыл бұрын
Thanks for the refresher. I hardly understood this when getting my undergrad degree and now that im working on my masters it came back to haunt me 🤣
@bgbg418
3 жыл бұрын
Wow I wish I found this in my first year. It would've saved me hours of lengthy abstract examples and confusion. Why do universities make things so unnecessarily complicated sometimes 🙄.
@aayushve426
6 ай бұрын
Great video as always !
@ZectonplaysMC
5 жыл бұрын
Dude i normally watch ur vids for fun but now i actually need help and i come back to ur channel😂
@Surya_Kiran_K
Жыл бұрын
I would attend every class of this guy 😭👍💓
@scar6073
Жыл бұрын
Thank you for explaining this in a straightforward manner, I FUCKING LOVE YOU!
@WhiteDotX
6 жыл бұрын
I just keeping learning a lot from you. Greetings from Mexico! Can you talk about set theory or keep doing number theory?
@blackpenredpen
6 жыл бұрын
Silvestre Frijol Cruz thank you!! I will focus on number theory, probability and combinatorics and calc.
@militantpacifist4087
2 жыл бұрын
This video has the most epic donut-math intro to be honest.
@sazsaiglesias
2 жыл бұрын
you saved my exam tomorrow..thank you
@liamcauquil6800
5 жыл бұрын
Hey, good video! Could you explain how 10 ≡ -2 became 10 ≡ 2 by adding 4 to the -2?
@liitutereuiui4687
3 жыл бұрын
I also want to know
@Nour_Ayasrah
3 жыл бұрын
too late, but if by any chance someone needs it later on, this is one way to think about it. note that if you are dealing with mod(n), any integer will be congruent to the set starting from 0 to n-1(i.e: {0,1,2,...,n-1}), so for mod(4) we have {0,1,2,3}, so now what happens if we add "4" or multiples of it to any of these? well, u go a full cycle/s so 0+4 = 0 mod(4), 1 + 2*4 = 1 mod(4) etc. so essentially inside the realm of mod(4) adding 4 is analogous to adding 0 in the normal arithmetic, does not change a thing. so -2 mod(4) = -2+4 mod(4) = 2 mod(4).
@azharuddin7013
2 жыл бұрын
@@Nour_Ayasrah when he says that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 does'nt have same remainders.Plz help
@Nour_Ayasrah
2 жыл бұрын
@@azharuddin7013 hey buddy, the first definition says that both numbers have the same remainder when divided by n, and that is true here. 2/4 = 0*4 + 2(this 2 here is the remainder) 10/4 = 2*4 + 2(again this is the remainder) since in both cases the remainder is 2, they are congruent
@erickarbieto8111
4 жыл бұрын
Eres un crack! Y todo lo digo en español, porque hasta en Latinoamerica disfrutamos de tus videos; en serio, aprendo muchísimo! Thank you!
@jeremyjakob9721
4 жыл бұрын
These are all essential notions for how modular arithmetic works, but perhaps misses at the heart of what is happening. Modular arithmetic by virtue of being "modular " means that there is some equivalence relation on the integers in Z. Z mod n can be viewed as the quotient map from Z to the set of elements partitioned by the equivalence relation "a is congruent to b mod n if (a-b) divides n or equivalently if a is congruent to kn +b. That is Z mod n partitions Z into "equivalence classes" defined by the above relations. This more general approach allows for better understanding of the role that modular arithmetic plays in both group and ring theory.
@faizzailan5936
3 жыл бұрын
this is the best number theory explanation, well done
@ayyagarisrinivas5082
4 жыл бұрын
Helpful man thanks ; )
@madhurimamohanty2867
3 жыл бұрын
Well in India there's an exam called NMTC where you have to learn this as a part of syllabus when you're in grade 6. By the way I'm of grade 6 and I enjoy watching your calculus lectures
@stevejob.417
2 жыл бұрын
how old is grade 6
@ghassanabdalsalam9938
2 жыл бұрын
thaaaaaaaaaaaaank you , amazing , I love your explanation
@michelletan7855
3 жыл бұрын
thank you so much! you are amazing to explain the modular arithmetic! thank you thank you!
@frankensteinapps9442
Жыл бұрын
Thanks man I was bit confused in equivalence relations when this came up , turns out I was interpreting it in a wrong way
@giantdad7
6 жыл бұрын
Please keep uploading Number Theory videos!
@blackpenredpen
6 жыл бұрын
ok!!!!!!!!
@itzmrinyy7484
3 ай бұрын
Thank you so mucj for this video! I was just watching an IMO prpblem solving video and i couldn't help but wonder what "mod(n)" meant.
@BentHestad
3 жыл бұрын
Very helpful! Thanks!!
@tcpudp1429
2 жыл бұрын
I just want to say thank you man, you really helped me out 😃
@shacharh5470
6 жыл бұрын
Congruence relations and their corresponding quotient sets (and groups, and spaces, etc) are some of the richest topics in maths, and modular congruence is one of the most useful and ubiquitous ones.
@WendyLee808
4 жыл бұрын
Having test next week, found this video this week. Thank you 😊 Always wanted to know the interpretation of the congruent notation.
@adhiyanthaprabhujeyashanka2091
Жыл бұрын
At @4:17 you said it is two on the left hand side, but it is actually 10, just a small error, but adds more value to your content if you take care to correct, between everything is clear sir 🔥🙏
@Gold161803
6 жыл бұрын
I have actually seen (mod 1) used. It was to denote the fractional part of a non-integer, but non-integers aren't being considered here
@woojason7119
4 жыл бұрын
thanks for your vdo you saved me from an algorithm course it looked me quite a long time to understand what is meant by a=b (mod n)
@zhangruoran
5 жыл бұрын
: D this is exactly what I taught my students.
@blackpenredpen
5 жыл бұрын
: )))))
@prestontao2
3 жыл бұрын
thanks this helped me pass my test
@AnayBhad
11 ай бұрын
thanks for this video helped me a lot.
@elijahseh7112
5 жыл бұрын
Can you please do a video on multiplicative inverse modular arithmetic? I fully understand the basic modular arithmetic but finding the multiplicative inverse in modular arithmetic just keeps going over my head!
@mahadhersi3754
2 жыл бұрын
Thank you professor BlackpenRedpen I appreciate you this amazing lesson.
@aaronvr_
4 жыл бұрын
yoo great tutorials/lessons love ur stuff keep em coming !!
@oborooizamisi1894
2 жыл бұрын
Amazing explanation, just what I needed
@lucasgparker
6 жыл бұрын
Congrats on the 100k!!
@Ebvardh
6 жыл бұрын
Lovely explanation. Helped me finally visualize this concept before you even did the examples.
@Ethan-mj6wy
6 жыл бұрын
Great video, loving all the number theory :)
@blackpenredpen
6 жыл бұрын
Thanks!!!
@abuhanifhanif3636
4 жыл бұрын
Thanks a lot from Bangladesh
@thundrking
5 жыл бұрын
Straight to the point.. thanks
@arandomguy9518
3 жыл бұрын
Got what I needed by 0:59 ...mad thanks 👍
@ignite21385
3 жыл бұрын
This equation was everything.
@MathForLife
6 жыл бұрын
Ahah, "killing all math":DDD
@blackpenredpen
6 жыл бұрын
Eightc yup!!!!
@blackpenredpen
6 жыл бұрын
And max, you can record an intro and send it to me via google drive so I can put it in my videos to let more ppl know about ur channel.
@MathForLife
6 жыл бұрын
blackpenredpen thanks!!
@nnnmmiiii6994
2 жыл бұрын
excellent explanation
@123luckeyman123
3 жыл бұрын
This is really helpful! Where is the number Theory section in your channel
@motivationalcomred
Жыл бұрын
summary: a = b mod m is known ads congrunce relation where a divides m and b divides m with same remainder and a is some constant times *m +b
@Phelly2
5 жыл бұрын
What the heck are you holding? A microphone? It looks like a psionic amplifier from the game System Shock 2. lol
@arnavanand8037
5 жыл бұрын
*T H E R M A L D E T O N A T O R*
@donaldbiden7927
5 жыл бұрын
Poke ball
@Lolnigaaaaaaaaa
2 жыл бұрын
Couldn’t learn this my whole life until I saw this. Damn please complete series on modular arithmetic please sir.
@sergioh5515
6 жыл бұрын
You make math so entertaining :)
@navster100
4 жыл бұрын
im doing proofs with modular congruence and my head is exploding
@chelseastewart6853
4 жыл бұрын
reviewing for a discrete math exam and this was such a clear and simple explanation, Reading the formal definitions makes so much sense after watching this. Thanks so much.
@AhmedAzhad
4 жыл бұрын
Thank you very much. Very well explained.
@jerrytsai9580
4 жыл бұрын
Very well explained. Thank you so much.
@utkarshraj3272
4 жыл бұрын
You are great. Thank You Very Much
@nathanielgabriel
5 жыл бұрын
Smooth explanation
@collin2628
4 жыл бұрын
thank you mr. pen
@Soumyayoutube
5 жыл бұрын
U made it so easy ! thanks @you
@avatarmh
4 жыл бұрын
This guy nailed it. However, you might like to think about congruence, blackpenredpen covered it. Clarifying and memorable. Now I can move onto some proofs that have been baffling me!
@danieljohannbutcher9927
4 жыл бұрын
The black ball looks like a prop from the movie parallel. Great explanation, weird microphone.
@Amine-gz7gq
3 ай бұрын
A 4:28, you haven't convinced me : 10 and -2 when divided by 4 don't have the same remainder (you get 2 for 10 and -2 for -2).
@michelle732mn
3 жыл бұрын
THANK YOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU! P.S. I laughed when you said mod 1 kills all the math lol
@AlgyCuber
6 жыл бұрын
H times i factorial
@blackpenredpen
6 жыл бұрын
Algy Cuber Hi!!
@blackpenredpen
6 жыл бұрын
PI(hi)
@yrcmurthy8323
5 жыл бұрын
Nice
@robertkissinger6050
4 жыл бұрын
Excellent explanation!
@marnierogers3931
2 жыл бұрын
Great video, would love some more examples to cement how to use :)
@Isac986
5 жыл бұрын
Excelente me salvaste de leer mucha álgebra, continua con el álgebra moderna que es bien interesante al igual que el calculo
@MathsOnlineVideos
2 жыл бұрын
Thanks a lot man. That helps a lot!
@antoinelunaire9462
4 жыл бұрын
Thanks a lot, brief and effective
@dikshabhise7480
3 жыл бұрын
great teaching🥰 I finally understand 👍
@GeorgeDCowley
4 жыл бұрын
Thanks for telling me that the brackets were important. I was just subtracting.
@AndDiracisHisProphet
6 жыл бұрын
When I explain division with remainder it is usually for 4th graders or so. I give examples like "what is 10 divided by 3" and the children, only knowing division when it "divides" would usually say it doesn't work. Then i give a follow up question "if you have 10 peaces of candy and 3 children, how can you divide the candy fair" and we discuss that it qould probably fair if every child would get three candy and then we have to figure out what we should do with the last peace. and the correct answer is, of course, that I get the last peace of candy. what else?
@blackpenredpen
6 жыл бұрын
I prefer donuts!
@AndDiracisHisProphet
6 жыл бұрын
10 donuts? May I refer to my other comment? :D
@blackpenredpen
6 жыл бұрын
AndDiracisHisProphet loll
@manojrajguru8852
6 жыл бұрын
u are the best professor..
@jasonshih3633
8 ай бұрын
Bro explained everything when my professor couldnt
@valentinejepkemei149
2 жыл бұрын
Thank you you are talented keep it up good work
@nikhilgupta6415
5 жыл бұрын
No one told me this! And neither I could understand anyone but now I can
@shreenidhhi8633
4 жыл бұрын
I have a doubt. From a=(k×n)+b Can we say this is similar to dividend =divisor × quotient +remainder
Пікірлер: 424