Proof: Infimum of {1/n} = 0 | Real Analysis
The infimum of the set containing all reciprocals of natural numbers has an infimum of 0. That is, 0 is the greatest lower bound of {1/n | n is natural}. We prove this infimum in today's real analysis lesson using the Archimedean Principle, which tells us that given any real number x, we can find a greater natural number. Proof of Archimedean Principle: • Proof: Archimedean Principle of Real Numbe... Definition of Supremum and Infimum of a Set: • Definition of Supremum and Infimum of a Se... Epsilon Definition of Supremum and Infimum: • Epsilon Definition of Supremum and Infimum... Real Analysis Playlist: • Real Analysis 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
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