MATH 242: Analysis 1 (McGill Final)

Currently Playing: Absolute Value Definition of a Bounded Sequence | 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 The definition of a bounded sequence is a very important one, and it relies on a sequence having a lower an upper bound. However, we can also state the definition of a bounded sequence with only a single bound - namely an upper bound on the absolute value of the terms of the sequence. If there exists a real number that is greater than or equal to the absolute value of every term in a sequence, then the sequence is bounded, and the converse is true as well. As in: if a sequence is bounded then there exists a real number greater than or equal to the absolute value of every term in the sequence. We prove this equivalent definition of a bounded sequence in today's real analysis video lesson! For our proof we need this very useful equivalence between an absolute value inequality and an inequality with no absolute values, here is the lesson on the proof of this equivalence: https://www.youtube.com/watch?v=X7GhczgUy7c Intro to Sequences: https://www.youtube.com/watch?v=YEiZWonJrOg What are Bounded Sequences? https://www.youtube.com/watch?v=hkCKQdAFLAw Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu