Monotonic Functions

Why

We can generalize the notion of real monotone functions to functions between any two sets with total partial orders.

Definition

Let $(A, \geq_A)$ and $(B, \geq_B)$ be two partially ordered sets. $f:A \to B$ is isotonic if it is order preserving and antitonic if it is order reversing. A function is monotonic if it is either antitonic or isotonic.¹

Examples²

1. Future editions may modify this terminology. ↩︎
2. Future editions will include. A nice example is monotonic matrix functions. ↩︎