Originally Posted by

**mybrohshi5** so i have a set S which contains {n+1} elements. Now I let $\displaystyle x $ be an element of S and let T = S \ {x}.

So now T is of size "n" and we know that T contains a max and min, namely $\displaystyle \alpha = max(T) $ and $\displaystyle \beta = min(T) $

if $\displaystyle x < \alpha $ then $\displaystyle \alpha $ is a maximum for S

if $\displaystyle x > \alpha $ then $\displaystyle x $ is a maximum for S

similar reasoning for minimum

Thus we have shown that S will always contain a max and min (whether that be x, $\displaystyle \alpha $ or $\displaystyle \beta $)

**Am I missing something?**