# New post in Supremum-and-infimum

June 29th, 2020

August 1st, 2022

August 1st, 2022

## For $B=\{|x-y|: x,y\in A\}$, show that $\sup B = \sup A - \inf A$ and find $\inf B$

December 31st, 2020

## Prove $\sup(|f|) - \inf(|f|) \leq \sup(f) - \inf(f)$ for bounded function $f$ on set $S$

October 16th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

## Prove that two sets A and B with $A \cap B=\emptyset$, $\sup A = \sup B$, $\sup A \notin A$ and $\sup B \notin B$ cannot exist.

January 26th, 2020

August 1st, 2022

August 1st, 2022

## Proof of the Archimedean property

February 18th, 2020

March 25th, 2020

## Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.

October 25th, 2020

## Closest point property of subset of Hilbert space - what are the conditions for infimum to be finite?

October 26th, 2020

## Condition For A Set Having A Smallest Element

December 21st, 2020

## Supremum of measurable functions

October 5th, 2020

August 1st, 2022

August 1st, 2022

April 10th, 2020

August 1st, 2022

August 1st, 2022

## there are only finitely many n with $v+ϵ<x_n$ and $2)$ there are infinitely many $n$ with $v−ϵ<x_n$

October 19th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

## infimum and supremum notation

January 16th, 2020