monotone function

Meaning

Noun

• A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).
• A function f : X→Y (where X and Y are posets with partial order "≤") with either: (1) the property that x ≤ y implies f(x) ≤ f(y), or (2) the property that x ≤ y implies f(y) ≤ f(x).
• A Boolean function with the property that switching any one input variable from 0 to 1 results either in no change in output or a change from 0 to 1.

Related

Similar words

• monotonic function

Broader meaning words

• function