English Dictionary

monotone function

noun

(calculus) 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 monotone function is a function that preserves the order of the elements in its domain.

意味（1）

(calculus) 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).

Where defined, the first derivative of a monotone function never changes sign, although it may be zero.

意味（2）

(order theory, mathematical analysis) 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).

意味（3）

(Boolean algebra) 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.