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The Bolzano-Weierstrass theorem Part 1

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We state and prove the Bolzano-Weierstrass theorem.
Категория: Образование
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Текстовые комментарии (26)
أنس رضى (11 дней назад)
Bolzano Weistrosphere
Beppe Nonantola (1 месяц назад)
Very clear indeed! Thanks
ajsdoa (4 месяца назад)
6:01 when you're talking, it sounds like you can just pick any x_k from the sequence in your subsequence with no particular pattern. As I've understood it, you couldn't just pick for instance {x_1,x_2,x_5,x_8,x_33,x_40,...}, just randomized numbers, I believe there has to be some kind of pattern like {x_2,x_4,x_6} for instance.
Alex Ware (4 месяца назад)
Very useful video!
Ankit Gothwal (5 месяцев назад)
Thanks man. This video helped me a lot...keep making more of such videos...keep it up
Dimple Garg (6 месяцев назад)
Waste of time
Shatakshi Sharma (6 месяцев назад)
Sir if we take set of rationals between 0 and 1 this is also infinite and bounded subset of R but has no limit points....so does bolzano weirstras theorem fails in this case??
qwer1234 (10 месяцев назад)
not entirely accurate, the set must be closed and bounded (ie. compact) for the weierstrass theorem to be applied. for example, 1<x<2 is a bounded set, with the sequence xk = {1.9,1.99,1.999,1.9999,1.99999,1.99999,1.9999999,....) being contained entirely within it, however no convergent subsequence can be obtained because it isn't closed.
mathIsART (11 месяцев назад)
The way you explain math. It's mesmerizing. It's beautiful. I have no words.
peeshooter (1 год назад)
This is totally irrelevant but you look quite like Freddie Highmore..
Robert Wilson III (1 год назад)
So basically, since the original sequence is bounded and the original sequence isn't convergent, you could just remove all the problem causing elements of the original sequence to therefore guarantee a convergent subsequence. You'd think textbook authors could just write what I've written above in their textbook plainly (since this is actually a simple concept), but they don't and consequently leave students confused. This really helps me out with that (1, 0) example. I was having trouble trying to understand how a bounded sequence could be divergent but this video cleared that up for me. Thanks.
Andres Franco Valiente (17 дней назад)
THANK U LOL
Yutong chen (1 год назад)
Love you! Really clear! Thanks for sharing :)
Shiying He (2 года назад)
really helpful! thank you!!!
Noor Na (2 года назад)
Every convergent sequence is bounded, but not every bounded sequence is convergent
J Yu (8 месяцев назад)
If a sequence is convergent, it is bounded. If bounded infinite set of real numbers contains an accumulation point A, then there exists a sequence in the set converging to A.
tolgahan21 (1 год назад)
Yes, I was just about to write that "Bolzano-Weierstrass Theorem: A bounded sequence of real numbers has a convergent subsequence" :)
Hugh Jones (2 года назад)
+Noor Na But every bounded sequence (in Rn) has a convergent subsequence. :-)
Nikola Tesla (2 года назад)
thanks, im from mexico. To my teacher i dont understand, he explain so fast and so abstrac some time XD
Parag Shah [USG] (2 года назад)
awesome...tysm
Ptolemy Pi (2 года назад)
Your videos are always very helpful.
Ahmad ElMoslimany (3 года назад)
Awesome!
Ruslan Jantayev (3 года назад)
Thanks !
Juan Sebastian Trujillo Garcia (3 года назад)
Cool man, thanks!
Mohammed Alabboodi (3 года назад)
Thanks to explain that. Please can you put some examples!!!
Oscar Castillo (4 года назад)
Thank You! the idea of bounded and this theorem make sense to me now!

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