Max

$M$ The highest number in a set. If it is in a set that is in an open interval like $[1,5)$, then there is no maximum

Definition

Let $S\subset R$ and $M\in R$, $M$ is the maximum of $S$ $⟺$

1. $M\in S$
2. $\forall x\in S,x\le M$ There is only one Supremum. They are unique.

Examples

$max\{1,5\}=5$

Maximum For Empty Set

There is no maximum for the empty set.