# 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.

## References

• 1 http://www.nist.gov/dads/HTML/strictlyIncreasing.htmlstrictly increasing,” from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
Title monotonically increasing MonotonicallyIncreasing 2013-03-22 12:22:35 2013-03-22 12:22:35 akrowne (2) akrowne (2) 10 akrowne (2) Definition msc 40-00 monotone increasing strictly increasing MonotonicallyDecreasing