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.

$\blacksquare$

Also see

• Min Operation is Idempotent