A function is said to be nondecreasing on an interval if for all , where . Conversely, a function is said to be nonincreasing on an interval if for all with .

Jeffreys, H. and Jeffreys, B. S. "Increasing and Decreasing Functions." §1.065 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 22, 1988.

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Weisstein, Eric W. "Nondecreasing Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NondecreasingFunction.html