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!
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.
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
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!
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.
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 🙄.
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.
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 🔥🙏
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
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!
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.
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.
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
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.
PLEASE MORE MODULAR ARITHMETIC! You're the best
Sergio H will do!!
I spent an hour trying to understand it from my book... 6 minute video is what i needed.
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!
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
This is by far the best explanation....IMO!...here I come....!!!!
thanks!
C# exercises led me here... and I ain't even mad. Awesome video!
Thanks blackpenredpen for teaching us this!
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.
just had a great and clear understanding this was the lecture i needed thanks a lot mate!!!
thankyou so much!! this really helped a lot 🥰🥰
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.
thank you so much! you are amazing to explain the modular arithmetic! thank you thank you!
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 🤣
Eres un crack! Y todo lo digo en español, porque hasta en Latinoamerica disfrutamos de tus videos; en serio, aprendo muchísimo! Thank you!
Your explanation is amazing. It is way better than my professor's! Thank you so much!
Our major instructor discussed this topic like using speed of light.... Boom finish!!
our instructor doesnt discuss to us hahahahahaha boom
Thank you sooo muchhh. Finally i understood this🤩 speciall in just 5 mins👏🏻🙏🏻
this is the best number theory explanation, well done
Dude i normally watch ur vids for fun but now i actually need help and i come back to ur channel😂
me staring at the modulos on my ia paper and a video from 6 years ago saved my life
(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
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 🙄.
Helpful man thanks ; )
This video was awesome! I'm so glad I found your channel. You have a new subscriber here.
thaaaaaaaaaaaaank you , amazing , I love your explanation
Great video as always !
This video has the most epic donut-math intro to be honest.
thanks this helped me pass my test
I would attend every class of this guy 😭👍💓
Got what I needed by 0:59 ...mad thanks 👍
Thank you for explaining this in a straightforward manner, I FUCKING LOVE YOU!
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)
you saved my exam tomorrow..thank you
I just want to say thank you man, you really helped me out
😃
Very helpful! Thanks!!
thanks for this video helped me a lot.
u are the best professor..
Straight to the point.. thanks
do you have my schedule or something ?? how do you always upload what I need. thanks man !
OH wow!! ; )
Thanks man I was bit confused in equivalence relations when this came up , turns out I was interpreting it in a wrong way
Thanks a lot from Bangladesh
i just realized he used a blue pen. this is beyond science
excellent explanation
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
Amazing explanation, just what I needed
Excelente me salvaste de leer mucha álgebra, continua con el álgebra moderna que es bien interesante al igual que el calculo
Great video, loving all the number theory :)
Thanks!!!
You are great.
Thank You Very Much
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.
Excellent explanation!
Smooth explanation
: D this is exactly what I taught my students.
: )))))
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.
You make math so entertaining :)
Please keep uploading Number Theory videos!
ok!!!!!!!!
Lovely explanation. Helped me finally visualize this concept before you even did the examples.
Thank you professor BlackpenRedpen I appreciate you this amazing lesson.
great teaching🥰 I finally understand 👍
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!!
Thank you you are talented keep it up good work
This equation was everything.
Thanks a lot, brief and effective
thank you mr. pen
Thank you very much. Very well explained.
Very well explained. Thank you so much.
U made it so easy ! thanks @you
Thanks a lot man. That helps a lot!
No one told me this! And neither I could understand anyone but now I can
Thanks it's so nice and useful 👏👏👏
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.
Best explanation ❤️❤️
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 🔥🙏
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
very good video and very good explanation!
Great video, would love some more examples to cement how to use :)
Waoo nice one lecture👍😊
Congrats on the 100k!!
Thank you for this video
Great Explaination sir 👍
11 grade student fom India
Please do a video on eigen values and eigen vectors
This is really helpful! Where is the number Theory section in your channel
THANK YOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU!
P.S. I laughed when you said mod 1 kills all the math lol
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!
Thank you😊
Having test next week, found this video this week. Thank you 😊 Always wanted to know the interpretation of the congruent notation.
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.
Thank you very much
very good explain
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!
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
Thank you so much! This video really helps me with number theories