monotonically increasing

A sequence $(s_n)$ , $s_n \in \mathbb{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.

Bibliography

1

``strictly increasing,'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.