Similarly, a real function is monotonically nonincreasing if
Compare this to monotonically decreasing.
Conflict note. In some contexts, such as , this is called monotonically decreasing (in turn, our “monotonically decreasing” is called “strictly decreasing”). This is unfortunately counter-intuitive, since a sequence or function that is “flat” (such as ) is somehow “decreasing.” Beware!
is monotonically nonincreasing. It is also monotonically decreasing.
is nonincreasing but not monotonically decreasing.
is nonincreasing (note that is nonnegative).
is not nonincreasing. It also happens to fail to be monotonically nondecreasing.
is not nonincreasing, rather it is nondecreasing (and monotonically increasing).
- 1 “http://www.nist.gov/dads/HTML/monotoncdecr.htmlmonotonically decreasing,” from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.
|Date of creation||2013-03-22 12:22:32|
|Last modified on||2013-03-22 12:22:32|
|Last modified by||akrowne (2)|