monotonic

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

• monotonically increasing

• monotonically decreasing

• monotonically nondecreasing

• monotonically nonincreasing

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 functions. Smooth (analytic) 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