Supremum
Definition
A real number $s$ is the supremum (a.k.a. least upper bound) for a set $A \subseteq \mathbb{R}$ if it meets the following two criteria:
$s$ is an upper_bound for $A$;
if $b$ is any upper_bound for $A$, then $s \leq b$.
A real number $s$ is the supremum (a.k.a. least upper bound) for a set $A \subseteq \mathbb{R}$ if it meets the following two criteria:
$s$ is an upper_bound for $A$;
if $b$ is any upper_bound for $A$, then $s \leq b$.