MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proving Bolzano-Weierstrass with Nested Interval Property | Real Analysis

Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Get the coolest math clothes in the world! https://mathshion.com/ Real Analysis course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook! https://amzn.to/3CMdgjI 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 of Nested Interval Property: https://youtu.be/bihVbul-pto Proof of Bolzano Weierstrass Theorem for Sequences (with Monotone Convergence Theorem): https://youtu.be/EGVNs0AxEKw Proof that x^n Converges when |x| is less than 1: (coming soon) Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu