Nice illustrations.

Really, really well done. If math was taught this way more people would take math courses.

Why no comments?

love your work thank you!

you explained in an animation what took many pages (and books) to understand

For the algo

wow

Good work Otis 👍

Bravo!!!

Hey bro, thanks for comming for our place yesterday! Im subscribe!

Sir , your explanation is amazing and Unique ! Thank you

felt like going to hogwarts

What is the name of the program that you used in this animation? And How i can make the animation? Can you tell me please?

please make more videos on such theorems. Thank you so much.

Just from the step by step animation display I can feel the extraordinary patience the maker(s) put in it. Unbelievably clear trace of thought.

This video is gold

It was best Nd best video of maths in my life.....I loved it.....

I’m still confused by the prof of closed. I understand B_r(x) is contained in the complement of K, but why we can claim the complement of K is opened? I think B_r(x) is just a small portion of the complement of K, right? Hope someone can correct me, thanks!

This is truly an amazing video! Clearest explanation of the C.B. Theorem I have seen. Thank you and hope to see you make more content. Subscribed.

woah !!

26:42 You select third cycle element in A as if it satisfied "x in A-g(B)", but the third cycle is in range of g(B)

At 3:36 its C of n- 1, why is it n-1 and not +1?

Simple yet beautiful proof! Thank you!

awesome video..just wanted to let u know that u are changing the world for the better in a small way

This is the best presentation I've seen of this classical result. Would love to see your take on some logic. Maybe try Gödel's incompleteness theorems or some independence results?

How can I make such wonderful animations?

This video should have a lot more views than it does. Outstanding production quality, I would have never thought that I would find such a good video on this subject!

Phlus 🤣

Awesome video Very easy to understand

I like that approach. A great way of teaching mathematics !!!!

Cool video!

Thank you !

This helped my so much, thanks!

There is an error, I believe, in the "Quick Check" that the open ball B_r(x) is contained in the complement of K (at around 9:30). In the sentence "Moreover, because ... is contained in every other set in S, ...", the words "is contained by" should be replaced by "contains". Apart from that, excellent video.

great video

Very well explained 🔥

I approve

This video was simply amazing. One of the best math videos I've seen in my entire life to be honest.

Amazing

Поскольку в большей части литературы число ноль входит в набор натуральных чисел, следует рассмотреть следующие формулы, чтобы доказать биекцию между (N^2) и (N): 1) f(x,y)=(2^x)(2y+1)-1 ; 2) f(x,y)=((x+y)(x+y+1)\2)+x

It was all great . thank you. i just wish the narration was a little slower and it didn't have breaks while being animated. like a slower uncut visualization. anyways ,thanks a lot for the great work and huge amount of effort.

Scared after watching this

You should create more of this video's. Excellent stuff.. Thanks

That's great video,many thanks

enjoyed this video and understood this funny proof thank you

I understand it that way: a and b share the factor of 2, so the fraction can be reduced to a fraction c/d where c = a/2 and d = b/2. Applying the same proof for c and d though states that they also share the the factor 2. And continuing like that a and b have to share an infinte amount of the factor 2, which is not possible. Thus sqrt(2) must be irrational.

Thank you!! Was having a hard time visualizing simply from the Johnsonbaugh book

This is a great video! Really appreciate the work that went behind this. If I may make one suggestion, it would be that instead of having a lot of animations, it would probably be better to have shorter animations between ideas, and less silent space. For example, from 23:03, there is an entire 15 seconds of silence while the animation plays out, which in my opinion breaks the attention of the student (especially if it is assumed that if a viewer has gotten this far into the video, would be familiar with the idea of an invective function.) In this specific case, having the arrows grow in parallel instead of sequentially might be better. However, I do understand that that might be more difficult to animate.

THANK YOU VERY MUCH

√(x1+x2)^2+(y1+y2)^2≤ √x1^2+x2^2 +√y1^2+y2^2please and how can i proove that please