A sequence or function is said to be monotonicPlanetmathPlanetmath if it is

Intuitively, this means that a monotone sequence can be thought of a “staircase” going either only up, or only down, with the stairs any height and any depth. The same goes for step functionsPlanetmathPlanetmath. Smooth (analyticPlanetmathPlanetmath) monotone functions are like “slopes,” either up or down at potentially varying steepnesess.

Title monotonic
Canonical name Monotonic
Date of creation 2013-03-22 12:22:43
Last modified on 2013-03-22 12:22:43
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 5
Author akrowne (2)
Entry type Definition
Classification msc 40-00
Synonym monotonically
Synonym monotone