MATH 242: Analysis 1 (McGill Final)

Currently Playing: Proof: Sequence Order Limit Theorem (Inequalities and Limits) | 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 🛍 Get 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/3CMdgjI We prove the order limit theorem for convergent sequences. This proves that convergent sequences and their limits relate to each other and real numbers as we'd expect. For example if a_n converges to a and b_n converges to b, and every a_n is less than or equal to each b_n, then a is less than or equal to b. This theorem summarizes how inequalities behave with limits. #realanalysis Definition of the Limit of a Sequence: https://www.youtube.com/watch?v=cTnlHZD5ss4 Limit Law for Difference of Convergent Sequences: https://youtu.be/ZlAT0_W4yP0 Proof that a Constant Sequence Converges to its Constant Value: https://www.youtube.com/watch?v=O-quXJi6-ws 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