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
Canonical name	MonotonicallyIncreasing
Date of creation	2013-03-22 12:22:35
Last modified on	2013-03-22 12:22:35
Owner	akrowne (2)
Last modified by	akrowne (2)
Numerical id	10
Author	akrowne (2)
Entry type	Definition
Classification	msc 40-00
Synonym	monotone increasing
Synonym	strictly increasing
Related topic	MonotonicallyDecreasing