monotonically decreasing

A sequence $(s_{n})$ is monotonically decreasing if

s_{m}<s_{n}\;\forall\;m>n

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

f(x)<f(y)\;\forall\;x>y

Compare this to monotonically nonincreasing.

Conflict note. In other context, such as [1], this is called strictly decreasing. When this is the case, “monotonically nonincreasing” is instead called “monotonically decreasing.”

References

1 “http://www.nist.gov/dads/HTML/strictlyDecreasing.htmlstrictly decreasing,” from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.

Title	monotonically decreasing
Canonical name	MonotonicallyDecreasing
Date of creation	2013-03-22 12:22:30
Last modified on	2013-03-22 12:22:30
Owner	akrowne (2)
Last modified by	akrowne (2)
Numerical id	8
Author	akrowne (2)
Entry type	Definition
Classification	msc 40-00
Synonym	monotone decreasing
Synonym	strictly decreasing
Related topic	MonotonicallyIncreasing