Non-Decreasing Function

Last updated Nov 1, 2022

Let $f: X \to Y$, where $X$ and $Y$ are totally ordered. Then $f$ is Non-decreasing if $\forall x, y \in X$:

$$x \leq y \Rightarrow f(x) \leq f(y)$$ Note that if $x > y$, we know that $y \leq x$ so $f(x) \geq f(y)$.