monotonically increasing

A sequence $(s_n)$, $s_n\in ℝ$ is called monotonically increasing if

$$s_m>s_n\forall m>n$$

Similarly, a real function $f(x)$ is called monotonically increasing if

$$f(x)>f(y)\forall x>y$$

Compare this to monotonically nondecreasing.

Conflict note. This condition is also sometimes called strictly increasing [1]. In such a context, “monotonically increasing” has the same meaning as monotonically nondecreasing.