MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: The Limit of a Sequence is Unique | Real Analysis

Support the production of this course by joining Wrath of Math to access all my Real Analysis videos plus lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out 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/4lNpyNN Business Inquiries: wrathofmathlessons@gmail.com A convergent sequence converges to exactly one limit. That is, the limit of a sequence is unique. We'll prove this by contradiction in today's real analysis video lesson. We assume our convergent sequence converges to a and b, and that they are distinct, as in the limit is not unique. We then pick a sufficiently small epsilon and apply the definition of convergence to force the terms of our sequence to eventually satisfy two contradictory inequalities. Intro to Sequences: https://www.youtube.com/watch?v=YEiZWonJrOg&list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli&index=14 Definition of the Limit of a Sequence: https://www.youtube.com/watch?v=cTnlHZD5ss4&list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli&index=15 Proof (-1)^n Diverges: https://youtu.be/nEBF2oIS9Dk Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu