Definition 2

Let E and F be two ordered sets. A mapping f of E into F is said to be strictly increasing (or strictly order-preserving) if the relation $x < y$ implies $f(x) < f(y)$; f is said to be strictly decreasing (or strictly order-reversing) if the relation $x < y$ implies $f(x) > f(y)$. A mapping of E into F is said to be strictly monotone if it is either strictly increasing or strictly decreasing.

Examples