A is closed and bounded subset of R. Which of the following exist? $\sup A$
$\inf A$
$\max A$
$\min A$
I Thought all of them exist! Since $\sup = \max$ and $\inf = \min$ if it's closed and bounded.
But the answer says otherwise. Why???
Can anyone please help? Thank you.

For a general bounded set $A$, the supremum and infimum exist by the completeness axiom. The example $A=(0,1)$ shows that the max and min need not exist.
In your example, however, since the set it closed it will contain its sup and inf, which will therefore be the max and min of the set. So you are correct.
