MATH 242: Analysis 1 (McGill Final)

Currently Playing: Supremum of the Union of Sets | Real Analysis

Support the production of this course by joining Wrath of Math to access exclusive and early videos, original music, plus the real analysis lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍️ Check out my math clothing store: https://mathshion.com/ We discuss the supremum of the union of finitely many and infinitely many nonempty above bounded sets. We'll see that the supremum of the union of finitely many nonempty above bounded sets is the maximum of the supremums of the individual sets. We prove this by induction. We then see the supremum of the union of infinitely many nonempty above bounded sets does not necessarily exist. #realanalysis Epsilon Definition of Supremum: https://youtu.be/lCpoEWJRYNk Real Analysis Course: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli Real Analysis Exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXAN05Gm3iNmpz9SkVfLNqC Get the textbook for this course! https://amzn.to/3CMdgjI ★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