monotonic function

Also known as monotone function, weakly monotonic function, weakly monotone function, decreasing or increasing function, increasing or decreasing function

function between ordered sets that preserves or reverses the given order

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Figure 1. A monotonically non-decreasing function Figure 2. A monotonically non-increasing function Figure 3. A function that is not monotonic

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.