Proving Bolzano-Weierstrass with Nested Interval Property | Real Analysis

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We prove the Bolzano Weierstrass theorem using the Nested Interval Property. The Bolzano-Weierstrass theorem states every bounded sequence has a convergent subsequence. We will construct a subsequence by bounding our sequence between M and -M, then creating an infinite sequence of nested intervals from which the terms of our subsequence will come. We prove this subsequence converges to prove the BW theorem. #realanalysis

Proof that x^n Converges when |x| is less than 1: (coming soon)

Credit to Understanding Analysis by Stephen Abbott, where I first read this proof, and whose model I followed for the presentation.

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Extremely clear. I read the textbook proof and my prof's lecture notes seven times and cannot comprehend—this video just used once. Very nice explanation, thank you!

cheyennehu

The perfect teacher on youtube. Thanks sir for explaining i have watched most of your videos on real analysis you are the great sir❤❤

AcpkaisarbaghYogeshkumar

Ahhhh finally I found a channel for the first chapter in Elementary Analysis !!!
thanks :)

tanishk

It is indeed a really cool proof. Thank you.

quriositysquared

First time watching one of your videos and I cant believe how well you explained everything! Thank you

itlos

This is a hell lot of work. Deserves far more respect and attention than the crap we see on social media

Bedoroski

This was amazing! I had trouble understanding why we converged at the end in the book's proof but this video explained it very clearly!

strncatt

Thank you sir for your great video on this topic . Your explanation is very clear !

wtt

Thank you so much ! I didn't get the whole demonstration but honestly it's a great one ❤

AviciaBT

Can you make a video on proving the stolz cesaro theorem ?

krasimirronkov

So can I use this Theorem to show whether a sequence can have both a convergent and non-convergent subsequence?

camilletimothy

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