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Real Function Sequence Monotonically Nondecreasing

1	Real Function
1	Sequence
5	Monotonically Nondecreasing

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Monotonically Increasing

A sequence , $s_n \in \mathbb{R}$ is called monotonically increasing if

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

Similarly, a real function is called monotonically increasing if

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

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.