Скачать с ютуб Definition of Supremum and Infimum of a Set | Real Analysis в хорошем качестве

Definition of Supremum and Infimum of a Set | Real Analysis

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:    • Epsilon Definition of Supremum and In...   Proof that suprema and infima are unique:    • Proof: Supremum and Infimum are Uniqu...   Proof the maximum of a set is the supremum:    • Proof: Maximum of a Set is the Suprem...   Absolute value inequality result we mention near the end of the lesson:    • Proof: A Useful Absolute Value Inequa...   Supremum and Infimum Example Exercises:    • Proof: Supremum of {1/n} = 1 | Real A...      • Supremum of the Union of Sets | Real ...      • Proof: Supremum of {1/n} = 1 | Real A...      • Proof: Minimum of a Set is the Infimu...      • Proof: Infimum of {1/n} = 0 | Real An...      • Prove Infimums Exist with the Complet...   Thanks to Nasser Alhouti, Robert Rennie, Barbara Sharrock, and Lyndon for their generous support on Patreon! ◆ Donate on PayPal: https://www.paypal.me/wrathofmath ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   I hope you find this video helpful, and be sure to ask any questions down in the comments! +WRATH OF MATH+ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / @emery3050