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
I wonder which professor took one hour for congruence 😅then for sure your whole syllabus time schedule gonna wasted..., ഒരു മയത്തിൽ ഒക്കെ ആവം കേട്ടോ ...
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!
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
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 🙏🙏
@@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.
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.
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.
(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.
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!
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 🙄.
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
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.
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 🔥🙏
I can guarantee that most people will confuse the activity shown as comparable to developing a conceptual understanding of modular congruence. If he provided any sort of discovery in which one could find the relativity of discrete mathematics while performing the procedures of modular arithmetics then we could satisfy the looming problem of: When and where have I seen this before? Instead, as is the case of 'cutting corners', he stressed his strategic competency while disregarding the importance of the methodical alternatives represented. Those people whom hate maths or find the language nonsensical and deceptive do so because oftentimes someone who is still learning to teach the subject(s) denotes pertinent information yet fails to instruct on the basis of that which is the significance of an ontology; implying that, the concepts which are introduced can be conferred to the relevancy of an instantaneous appreciation by others. Per inference, everyone not exploring a career as a mathematician is ignoring the facts of exercises of the discipline. Why teach math while you are not becoming a mathematician?
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).
@@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
@@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
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.
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!
Hey bro ! Maybe I’m the latest one for this video but I want you to solve a math problem Here it is! Prove that: 1•3•5•...•2013+2•4•6•....•2014 is a multiple of 2015 I hope you see my comment and solve it for me. Thank you !
@blackpenredpen Hi, when you say that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 doesn't have same remainders.Plz help
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!
What donuts are those?
The heart attack kind of donuts.
I meant to ask where they are from
Heaven
Look like Krispy Kreme.
Kevin got it!!
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
same
so fucking dmn right
True
True. I am right now going through the same experience.
I wonder which professor took one hour for congruence 😅then for sure your whole syllabus time schedule gonna wasted..., ഒരു മയത്തിൽ ഒക്കെ ആവം കേട്ടോ ...
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!
Basically you throw out the quotient and keep the remainder. It's periodic math like the roots of a trig function.
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
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 🙏🙏
Some teachers in universities: 2h lecture
blacklenredpen: 6minutes
Too right mate, plus we can repay bprp's videos as often as we like.
He is just explaining the procedure not the theory, origins or proof
@@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.
PLEASE MORE MODULAR ARITHMETIC! You're the best
Sergio H will do!!
Your ability to change the marker you’re writing with so fast is amazing...
I read this comment and watched the video again just because of this. lmao. Wow! You were not joking.
I spent an hour trying to understand it from my book... 6 minute video is what i needed.
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.
Why is this video 2Pi minutes long ?
It's Tau
Burn!
2π=6
@@ansper1905 😑😑😑3.14159265358979323846264338
...
In can not be 3😐
@@sieger358 tell that to engineers
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.
(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.
bro you really came through i was having trouble understanding that claim
Omg saving my grade once again. God bless you. Wish you had a patreon...
For those of you watching this in the future:
He does!
www.patreon.com/blackpenredpen
I learned more from this guy than from my entire math class xDDD
My math teacher made this look like rocket science...
same hahahahahahahhaha
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!
This is by far the best explanation....IMO!...here I come....!!!!
thanks!
Thanks blackpenredpen for teaching us this!
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 🙄.
You should do more number theory, especially stuff like Euler’s totient function (since it’s my favorite subject ;D)!
I will. In the meantime, you can check out Max's videos here: ruclips.net/channel/UCP-ZCMz7olJPUI78b_bQrvQvideos?disable_polymer=1
C# exercises led me here... and I ain't even mad. Awesome video!
thank you so much! you are amazing to explain the modular arithmetic! thank you thank you!
Our major instructor discussed this topic like using speed of light.... Boom finish!!
our instructor doesnt discuss to us hahahahahaha boom
Your explanation is amazing. It is way better than my professor's! Thank you so much!
you saved my exam tomorrow..thank you
thankyou so much!! this really helped a lot 🥰🥰
Got what I needed by 0:59 ...mad thanks 👍
I would attend every class of this guy 😭👍💓
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 🤣
Thanks a lot from Bangladesh
Great video as always !
just had a great and clear understanding this was the lecture i needed thanks a lot mate!!!
this is the best number theory explanation, well done
Eres un crack! Y todo lo digo en español, porque hasta en Latinoamerica disfrutamos de tus videos; en serio, aprendo muchísimo! Thank you!
This video has the most epic donut-math intro to be honest.
Helpful man thanks ; )
This video was awesome! I'm so glad I found your channel. You have a new subscriber here.
Thank you for explaining this in a straightforward manner, I FUCKING LOVE YOU!
Dude i normally watch ur vids for fun but now i actually need help and i come back to ur channel😂
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
how old is grade 6
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.
thanks this helped me pass my test
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 🔥🙏
I can guarantee that most people will confuse the activity shown as comparable to developing a conceptual understanding of modular congruence. If he provided any sort of discovery in which one could find the relativity of discrete mathematics while performing the procedures of modular arithmetics then we could satisfy the looming problem of: When and where have I seen this before? Instead, as is the case of 'cutting corners', he stressed his strategic competency while disregarding the importance of the methodical alternatives represented. Those people whom hate maths or find the language nonsensical and deceptive do so because oftentimes someone who is still learning to teach the subject(s) denotes pertinent information yet fails to instruct on the basis of that which is the significance of an ontology; implying that, the concepts which are introduced can be conferred to the relevancy of an instantaneous appreciation by others. Per inference, everyone not exploring a career as a mathematician is ignoring the facts of exercises of the discipline. Why teach math while you are not becoming a mathematician?
Very helpful! Thanks!!
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
thaaaaaaaaaaaaank you , amazing , I love your explanation
Great Explaination sir 👍
11 grade student fom India
Hey, good video! Could you explain how 10 ≡ -2 became 10 ≡ 2 by adding 4 to the -2?
I also want to know
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).
@@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
@@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
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.
Straight to the point.. thanks
I just want to say thank you man, you really helped me out
😃
do you have my schedule or something ?? how do you always upload what I need. thanks man !
OH wow!! ; )
u are the best professor..
Please keep uploading Number Theory videos!
ok!!!!!!!!
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!
Hey bro ! Maybe I’m the latest one for this video but I want you to solve a math problem
Here it is!
Prove that: 1•3•5•...•2013+2•4•6•....•2014 is a multiple of 2015
I hope you see my comment and solve it for me. Thank you !
THANK YOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU!
P.S. I laughed when you said mod 1 kills all the math lol
Killing all the numbers you eat😂
im doing proofs with modular congruence and my head is exploding
excellent explanation
Amazing explanation, just what I needed
Thanks man I was bit confused in equivalence relations when this came up , turns out I was interpreting it in a wrong way
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)
Smooth explanation
Ahah, "killing all math":DDD
Eightc yup!!!!
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.
blackpenredpen thanks!!
Excellent explanation!
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
thanks for this video helped me a lot.
You make math so entertaining :)
: D this is exactly what I taught my students.
: )))))
Great video, loving all the number theory :)
Thanks!!!
Congrats on the 100k!!
This is really helpful! Where is the number Theory section in your channel
H times i factorial
Algy Cuber Hi!!
PI(hi)
Nice
I just keeping learning a lot from you.
Greetings from Mexico!
Can you talk about set theory or keep doing number theory?
Silvestre Frijol Cruz thank you!! I will focus on number theory, probability and combinatorics and calc.
Lovely explanation. Helped me finally visualize this concept before you even did the examples.
Thank you professor BlackpenRedpen I appreciate you this amazing lesson.
@blackpenredpen Hi,
when you say that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 doesn't have same remainders.Plz help
Actually, they do. 10 divided by 4 is 2 with a remainder of 2. 2 divided by 4 is zero with a remainder of 2. Hope this helps.
i just realized he used a blue pen. this is beyond science
great teaching🥰 I finally understand 👍
You are great.
Thank You Very Much
Thank you you are talented keep it up good work
Thanks a lot man. That helps a lot!
very good video and very good explanation!
Waoo nice one lecture👍😊
thank you mr. pen
This equation was everything.
Thank you very much. Very well explained.
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!
Thanks for telling me that the brackets were important.
I was just subtracting.
What the heck are you holding? A microphone? It looks like a psionic amplifier from the game System Shock 2. lol
*T H E R M A L D E T O N A T O R*
Poke ball
Thanks a lot, brief and effective
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.
Mom I'm becoming a mathematician
Lol
Very well explained. Thank you so much.
I have a doubt.
From a=(k×n)+b
Can we say this is similar to
dividend =divisor × quotient +remainder
Best explanation ❤️❤️
When i first saw a and b in math i thought a and b meant 1 and 2
The black ball looks like a prop from the movie parallel. Great explanation, weird microphone.