monotone function

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(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).

日本語の意味

定義域（実数の部分集合）において、入力値が大きくなると常に出力値が大きくなるか、または常に小さくなる（すなわち、x ≤ yならば f(x) ≤ f(y) または x ≤ yならば f(x) ≥ f(y)）性質を持つ関数。これは単調増加関数あるいは単調減少関数とも呼ばれます。

英語の意味

(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).

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A monotone function on a subset of the real numbers either never decreases or never increases as its independent variable increases.

実数の部分集合上の単調関数は、独立変数が増加するにつれて決して減少しないか、あるいは決して増加しない。

詳細

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.

詳細

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.

monotone functions （ plural ）