Watch and track your favorite playlist.
Curated by: Anna1.618 (104 videos)
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 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 Proof Every Sequence has a Monotone Subsequence (Monotone Subsequence Theorem): https://youtu.be/00I5Qy8fd68 Proof of Monotone Convergence Theorem: https://youtu.be/4NURDmE79VU Bolzano-Weierstrass Theorem for Sequences: (coming soon) Proving Bolzano-Weierstrass with Nested Intervals: https://youtu.be/pNRl9dmZ2LA Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu