MATH 242: Analysis 1 (McGill Final)

Currently Playing: Lipschitz Functions and Uniform Continuity | 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 my math fashion brand! 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 We introduce Lipschitz functions/Lipschitz continuity. A function is Lipschitz on a set if the magnitudes of the slopes of its secant lines on the set are bounded above by some fixed positive number. We'll prove Lipschitz functions are always uniformly continuous and see an examples of a uniformly continuous function which fails to be Lipschitz. #realanalysis Uniform Continuity Explained: https://youtu.be/MmxtJwr3Kws ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Outro music by Ben Watts: https://crayon-angel.bandcamp.com/music Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 0:13 Definition of Lipschitz Continuity 1:06 Lipchitz Example 1:40 Lipchitz Implies Uniform Continuity 3:56 Uniform Continuity Doesn't Imply Lipschitz 7:42 Conclusion