Definition:Max Operation

Definition
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}$

Notation
The notation $\max \set {x, y}$ is frequently seen for $\map \max {x, y}$.

This emphasises that the operands of the max operation are undifferentiated as to order.

Some sources use the notation $x \vee y$ for $\map \max {x, y}$.

Also see

 * Definition:Min Operation