# Category:Max Operation

Let $\struct {S, \preceq}$ be a totally ordered set.
The max operation is the binary operation on $\struct {S, \preceq}$ defined as:
$\forall x, y \in S: \map \max {x, y} = \begin{cases} y & : x \preceq y \\ x & : y \preceq x \end{cases}$