#### Alfredo Dawlabany

##### New member

- Joined
- Aug 22, 2017

- Messages
- 45

Prove that Sup B = Sup A - Inf A.

I tried to solve it but didn't know what to do

I said that if A is a bounded set then \(\displaystyle A\subset \left [InfA,SupA\right ]\)

\(\displaystyle \Rightarrow x,y \in \left [ InfA,SupA \right ]\)

so we have \(\displaystyle InfA\leqslant x\leqslant SupA\) and \(\displaystyle InfA\leqslant y\leqslant SupA\)

Am I going right ? If yes how would I continue ?