MATH 242: Analysis 1 (McGill Final)

Currently Playing: What are Monotone Sequences? | 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 introduce monotone sequences, monotone increasing, and monotone decreasing sequences, with plenty of examples and non-examples. We'll see how a sequence can be both increasing and decreasing, and we'll see some equivalent characterizations of increasing and decreasing sequences. #RealAnalysis We'll also discuss what it means for a sequence to be strictly increasing and strictly decreasing, and what it means to be eventually increasing and eventually decreasing. Proof of Monotone Convergence Theorem: https://youtu.be/4NURDmE79VU Fun Example of Monotone Convergence Theorem: https://youtu.be/AuvBS7UKxqU Monotone Sequence Converges if it has Convergent Subsequence: https://youtu.be/BZ-LQpz5EBc Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu