Watch and track your favorite playlist.
Curated by: Anna1.618 (104 videos)
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 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/4lNpyNN Business Inquiries: wrathofmathlessons@gmail.com The axiom of completeness fills in the holes of the rationals to give us the reals by guaranteeing that nonempty sets that are bounded above have least upper bounds, called supremums. The axiom of completeness does not address infimums, or greatest lower bounds - but today we see that the axiom of completeness in fact implies the existence of infimums for bounded below sets, and we prove this. #realanalysis Supremum and Infimum: https://youtu.be/QRGIhqz9vh4 Epsilon Definition of Supremum and Infimum: https://www.youtube.com/watch?v=lCpoEWJRYNk Proof the maximum of a set is the supremum: https://www.youtube.com/watch?v=5bLaGzeTMkY ★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 ● Facebook: https://www.facebook.com/WrathofMath