MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Limit Law for Difference of Convergent 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 prove the limit law for the difference of convergent sequences. If a_n converges to a and b_n converges to b, then the sequence a_n - b_n converges to a - b. As in, the difference of convergent sequences converges to the difference of their limits. This is a fairly straightforward proof using the epsilon definition of a convergent sequence, and is very similar to the proof of the limit law for the sum of convergent sequences. 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