DEF-UPB. Upper and Lower Bound.
Let $(X,\leq)$ be a preordered set. Let $A\subseteq X$ and $a\in X$.
$a$ is an upper bound of $A$, if
\[\forall x\in A : x\leq a.\]$a$ is a lower bound of $A$, if
\[\forall x\in A : a\leq x.\]
DEF-UPB. Upper and Lower Bound.
Let $(X,\leq)$ be a preordered set. Let $A\subseteq X$ and $a\in X$.
$a$ is an upper bound of $A$, if
\[\forall x\in A : x\leq a.\]$a$ is a lower bound of $A$, if
\[\forall x\in A : a\leq x.\]