MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Convergent Sequence is Bounded | 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 Any convergent sequence must be bounded. We'll prove this basic result about convergent sequences in today's lesson. We use the definition of the limit of a sequence, a useful equivalence involving absolute value inequalities, and then considering a maximum and minimum will help us find an upper and lower bound to use for our proof that a convergent sequence is bounded! What are Bounded Sequences? https://youtu.be/hkCKQdAFLAw A Useful Absolute Value Inequality: https://youtu.be/X7GhczgUy7c Definition of the Limit of a Sequence: https://youtu.be/cTnlHZD5ss4 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