The Epsilon Criterion for Supremum and Infimum | Examples of Sup and Inf | Real Analysis | Lecture 4

This lecture in Real Analysis covers the epsilon criterion for supremum and infimum. Examples of proofs about supremum and infimum are provided.

00:00 Introduction
00:24 Review of the definitions of supremum and infimum
02:24 The statement of the epsilon criteria for supremum and infimum
06:38 Example: proof of the statement sup{(n+1)/n: n \in N}=1
13:03 Example: proof that the maximal element is the supremum

Related lecture:

Axioms of Real Numbers | Part 3: The Completeness Axiom | Sup and Inf | Real Analysis | Lecture 3

All lectures in Real Analysis:

Real ANALYSIS -- Modern ANALYSIS -- Advanced CALCULUS

[bwax]

Very concise, I was able to follow along

[valeriereid]

Thank you for this excellent lecture. Just wondering if you have one that explains subsequences and the Bolzano-Weierstrass theorem and the epsilon neighbourhood of a.

[giftumoren]

I love this channel, sooo much
Thanks ma for the precise Lecture

[sahasra]

I have a doubt on Ex1. In the statement where you wrote n*ε>1 works for ε>0, what happens if ε=0.1 for example? Wouldn't nε be less than 1. I'm slightly confused about this.