Monotonic function

"Monotonicity" redirects here. For information on monotonicity as it pertains to voting systems, see monotonicity criterion. For information on monotonicity as it pertains to logical systems, see Monotonicity of entailment.

"Monotonic" redirects here. For other uses, see Monotone (disambiguation).

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.