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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).
Definition source: English Wiktionary via Wiktextract
Topics: calculus, mathematics, sciences
Examples
- Where defined, the first derivative of a monotone function never changes sign, although it may be zero.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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).
Definition source: English Wiktionary via Wiktextract
Topics: mathematical-analysis, mathematics, order-theory, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.
Definition source: English Wiktionary via Wiktextract
Qualifier: Boolean algebra
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
10 source translations are retained for this English entry.
-
Bulgarian:
монотонна функция
(monotonna funkcija)
— calculus: real function that either never decreases or never increases
-
German:
monotone Funktion
— calculus: real function that either never decreases or never increases
-
Serbo-Croatian:
monotona funkcija
— calculus: real function that either never decreases or never increases
-
Spanish:
función monótona
— calculus: real function that either never decreases or never increases
-
Turkish:
monoton fonksiyon
— calculus: real function that either never decreases or never increases
-
German:
monotone Funktion
— order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)
-
Serbo-Croatian:
monotona funkcija
— order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)
-
Spanish:
función monótona
— order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)
-
Turkish:
monoton fonksiyon
— order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)
-
Bulgarian:
монотонна функция
(monotonna funkcija)
— Boolean function such that switching an input from 0 to 1 either does not change the output or changes it from 0 to 1
