Heine-Borel Theorem

[@Labroidas]

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!

[@ranjumarkam4925]

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

[@pulkitnijhawan653]

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

[@abhisheksinghsengar6905]

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

[@wilsojtheblue2881]

Cool video!

[@EDITsRRMDS]

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

[@gdsfish3214]

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

[@TranquilSeaOfMath]

Nice illustrations.

[@dongchenwang454]

Nice video and elegant proof. Thanks!!!

[@miawong3024]

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

[@abhisheksinghsengar6905]

woah !!

[@isabelleanna2573]

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

[@yrstrulyrajan566]

How can I make such wonderful animations?

[@woodin_cardinal-4863]

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?

[@kollinpoindexter8859]

Great concept to use animation to picture out these theorems. I have been studying them by drawing out set on black boards and applying definitions and theorems from my book, so seeing them drawn out for me and following along has really sped up the process of understanding material.

[@tankesprang]

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.

[@philipvuong7373]

Thanks!

[@maxpercer7119]

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

[@maryamjamali1739]

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.

[@ArisCheeseGod]

😍

[@divyanshparmar5840]

U explained it very well man👍👌

[@saraahmed8430]

very nice and interesting explanation thank you very much

[@timkris1574]

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!

[@amritlohia8240]

It's effectively a proof by contradiction. We want to show that the complement of K is open (i.e. that K is closed), so we assume for contradiction that there is x in the complement of K such that no open ball B_r(x) is contained in the compliment of K.

[@devanarayanababu1996]

For the algo

[@fakeaccount702]

Very well explained 🔥