Max Operation is Idempotent

Theorem
The max operation operation is idempotent:


 * $\map \max {x, x} = x$

Proof
Follows immediately from the definition of max operation:


 * $\map \max {a, b} = \begin {cases} b & : a \le b \\ a & : b \le a \end {cases}$

Setting $x = a = b$ returns the result.

Also see

 * Min Operation is Idempotent