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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.
- 1
- ``strictly increasing,'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
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