MATH 242: Analysis 1 (McGill Final)

Currently Playing: Detailed Proof of the Monotone Convergence Theorem | 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 🛍 Check out my math clothing store: 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 a detailed version of the monotone convergence theorem. We'll prove that a monotone sequence converges if and only if it is bounded. In particular, if it is increasing and unbounded, then it diverges to positive infinity, if it is increasing and bounded, then it converges to the supremum of the set of sequence values. If a sequence is decreasing and unbounded, then it diverges to negative infinity, if it is decreasing and bounded then it converges to the infimum of the set of sequence values. #RealAnalysis A Fun Example Using the Monotone Convergence Theorem: https://youtu.be/AuvBS7UKxqU Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu