Short Proof of Bolzano-Weierstrass Theorem for Sequences | Real Analysis

Every bounded sequence has a convergent subsequence. This is the Bolzano-Weierstrass theorem for sequences, and we prove it in today's real analysis video lesson. We'll use two previous results that make this proof short and easy. First is the monotone subsequence theorem, stating that every sequence has a monotone subsequence. Then we finish things off with the monotone convergence theorem, telling us a monotone sequence converges if and only if it is bounded. #RealAnalysis

Bolzano-Weierstrass Theorem for Sequences: (coming soon)

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[luojasmine]

Thank you so mcuh! Looking forward to the video Proving Bolzano-Weierstrass with Nested Intervals

[_Phoenix]

Way more intuitive proof than the one using NIP.

[turokg]

way better proof than the long one imo. more intuitive

[WrathofMath]

Check out the proofs of the two results we use in this video!

[shivanjanborgohain]

hey, please make a playlist on infinite series

[sussyballz]

im in the 11th grade and was assigned to make a presentation on this, great explanation