# New post in Supremum-and-infimum

## Given $A, B \subset R$, both non-empty, show that $\inf{(A \cup B)} = \min{\{\inf{A}, \inf{B}\}}$

September 24th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

## Infimum of the Ky Fan metric achieved

September 12th, 2020

## let $A_1, A_2, A_3, \dots$ be a collection of nonempty sets, each of which is bounded above. $(a)$ Find a formula for $\sup(A_1\cup A_2)$.

September 7th, 2020

August 1st, 2022

August 1st, 2022

## Pointwise infimum of an arbitrary collection of upper semicontinuous functions is upper semicontinuous

October 10th, 2020

August 1st, 2022

August 1st, 2022

## Given that $x,y,z$ are positive reals such that $xyz=32$.What is the minimum value of $x^2+4xy+4y^2+2z^2$.

October 8th, 2020

May 9th, 2020

August 1st, 2022

August 1st, 2022

## Show that: $\inf(A+B) = \inf(A)+ \inf(B)$

December 14th, 2020

August 1st, 2022

July 19th, 2020

August 1st, 2022

August 4th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

April 15th, 2021

August 1st, 2022

## Convex function can be written as supremum of some affine functions

October 10th, 2020

May 5th, 2021