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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 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 What are suprema and infima of a set? This is an important concept in real analysis, we'll be defining both terms today with supremum examples and infimum examples to help make it clear! In short, a supremum of a set is a least upper bound. An infimum is a greatest lower bound. It is easily proven that we can refer to "the supremum" and "the infimum" of a set because if they exist they are unique. Epsilon Definition of Supremum and Infimum: https://www.youtube.com/watch?v=lCpoEWJRYNk Proof that suprema and infima are unique: https://www.youtube.com/watch?v=BXwsiEI133M Proof the maximum of a set is the supremum: https://www.youtube.com/watch?v=5bLaGzeTMkY Absolute value inequality result we mention near the end of the lesson: https://www.youtube.com/watch?v=X7GhczgUy7c ◆ Donate on PayPal: https://www.paypal.me/wrathofmath ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu