Definition:Min Operation

Definition
Let $\struct {S, \preceq}$ be a totally ordered set.

The min operation is the binary operation on $\struct {S, \preceq}$ defined as:
 * $\forall x, y \in S: \map \min {x, y} = \begin {cases}

x & : x \preceq y \\ y & : y \preceq x \end {cases}$

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

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

Some sources use the notation $x \wedge y$ for $\map \min {x, y}$.

Also see

 * Definition:Max Operation