i am stuck in this simple but foggy problem. i need to prove or show that the min and sup are unique if they exist.
$A$ is a nonempty set and $B$ is nonempty subset of $A$. i am trying to show that the $minB$ and $supB$ are unique once they exist.
my start is this:
$minB \Longleftrightarrow \forall_{x \in B} \exists_{m \in B} m \leq x$
if there is $m' \in B$ then $m \leq m' \leq x $
but i have bad feeling doing this, it seems to be not enough proved.
Can someone help me please with this? Thanks alot