Min Operation is Idempotent

Theorem

The min operation operation is idempotent:

$\map \min {x, x} = x$

Proof

Follows immediately from the definition of min operation:

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

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

$\blacksquare$

Also see

• Max Operation is Idempotent