MATH 242: Analysis 1 (McGill Final)

Currently Playing: Uniform Continuity on Compact Sets | 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 prove that if f is a continuous function on a compact set K, then f is in fact uniformly continuous on K. Thus, on compact sets, uniform continuity and ordinary continuity are equivalent. To prove this fact, we'll use the sequential criterion for the absence of uniform continuity. #realanalysis Uniform Continuity Explained: https://youtu.be/MmxtJwr3Kws Sequential Criterion of Absence of Uniform Continuity: https://youtu.be/L9XZc9m4yXg ★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