Prove Infimums Exist with the Completeness Axiom | Real Analysis

The completeness axiom asserts that if A is a nonempty subset of the reals that is bounded above, then A has a least upper bound - called the supremum. This does not say anything about if greatest lower bounds - infimums exist for sets that are bounded below, but we can use the completeness axiom to prove infimums exist too! #RealAnalysis #Math 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   ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / @emery3050