Definition:Min Operation

Let $$\left({S, \preceq}\right)$$ be a totally ordered set.

The min operation is the binary operation on $$\left({S, \preceq}\right)$$ defined as:

\forall x, y \in S: \min \left({x, y}\right) = \begin{cases} x: & x \preceq y \\ y: & y \preceq x \end{cases} $$

Notation
The notation $$\min \left\{{x, y}\right\}$$ is frequently seen for $$\min \left({x, y}\right)$$.

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