MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Limit Law for Quotient 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 quotient 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, provided that b isn't 0, and each b_n is not 0. Put simply, the quotient of convergent sequences converges to the quotient of their limits. This is a slightly tricky proof using the epsilon definition of a convergent sequence, and some fun absolute value inequality manipulations! Proof of Triangle Inequality Theorem: https://www.youtube.com/watch?v=051WWg9twO0 Proof of Reverse Triangle Inequality: https://www.youtube.com/watch?v=4OmIRB5Zv-4 Definition of the Limit of a Sequence: https://www.youtube.com/watch?v=cTnlHZD5ss4 What are Bounded Sequences? https://www.youtube.com/watch?v=hkCKQdAFLAw Proof that a Convergent Sequence is Bounded: https://www.youtube.com/watch?v=7N-4XZlxBho ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu