Prove Infimums Exist with the Completeness Axiom | Real Analysis

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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!

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thank you for the clear explanation, you saved my brain from processing 15 slides of presentation from my professor.

P.S Can I just say, I've never seen someone so enthusiastic about proving before! Really helped keep my attention . Keep it up brother!

queenbizmillah
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Your my best lecturer ever. Thanks for always being there for me

EgonuPatrick
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I've started studying university level math after a long break from math... Your videos have provided me so much clarity and I am incredibly grateful! Thanks so much! (:(:(:

katherineberger
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Many thanks for this important lecture! 👍

punditgi
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Thanks a lot sir, I was dying while trying to understand it using Apostol, and you made my life much easier.

nightsky
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Nicely done! Will you be covering lim sup and lim inf at some point?

tomkerruish
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Awesome video! :) I like this presentation
And this i hope helps students a lot!

aashsyed
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Amazing. Thank you so much for your videos🙏

AvivNoah-hw