monotonically nondecreasing

A sequence $(s_{n})$ (with real elements) is called monotonically nondecreasing if

 $s_{m}\geq s_{n}\;\forall\;m>n$

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

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

Compare this to monotonically increasing.

Conflict note. In other contexts, such as [1], this is called monotonically increasing (despite the fact that the sequence could be “flat.” In such a context, our definition of “monotonically increasing” is called strictly increasing.

References

• 1 http://www.nist.gov/dads/HTML/monotoncincr.htmlmonotonically increasing,” from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
Title monotonically nondecreasing MonotonicallyNondecreasing 2013-03-22 12:22:38 2013-03-22 12:22:38 akrowne (2) akrowne (2) 8 akrowne (2) Definition msc 40-00 monotone nondecreasing MonotonicallyNonincreasing