"monotone function" meaning in All languages combined

See monotone function on Wiktionary

Noun [English]

Forms: monotone functions [plural]
Head templates: {{en-noun}} monotone function (plural monotone functions)
  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). Categories (topical): Calculus, Functions Synonyms (function that either never decreases or never increases): monotonic function Translations (calculus: real function that either never decreases or never increases): monotone Funktion [feminine] (German), monotona funkcija [feminine] (Serbo-Croatian), monoton fonksiyon (Turkish)
    Sense id: en-monotone_function-en-noun-vrgD6lcF Topics: calculus, mathematics, sciences Disambiguation of 'function that either never decreases or never increases': 73 13 14 Hyponyms (function that never decreases as its independent variable increases): nondecreasing function, monotone nondecreasing function, monotonic nondecreasing function, monotonically nondecreasing function, increasing function, monotone increasing function, monotonic increasing function, monotonically increasing function Hyponyms (function that never increases as its independent variable increases): nonincreasing function, monotone nonincreasing function, monotonic nonincreasing function, monotonically nonincreasing function, decreasing function, monotone decreasing function, monotonic decreasing function, monotonically decreasing function Disambiguation of 'function that never decreases as its independent variable increases': 77 11 11 Disambiguation of 'function that never increases as its independent variable increases': 78 11 11 Disambiguation of 'calculus: real function that either never decreases or never increases': 52 18 30
  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). Categories (topical): Mathematical analysis
    Sense id: en-monotone_function-en-noun-h7rjGnkW Topics: mathematical-analysis, mathematics, order-theory, sciences
  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.
    Sense id: en-monotone_function-en-noun-VDXIrdjZ Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms with non-redundant non-automated sortkeys Disambiguation of English entries with incorrect language header: 31 29 40 Disambiguation of English entries with topic categories using raw markup: 36 17 48 Disambiguation of English terms with non-redundant non-automated sortkeys: 30 26 44
The following are not (yet) sense-disambiguated
Synonyms: monotonic function Hypernyms: function Hyponyms: isotone function [order-theory, mathematics, sciences], order-preserving function [order-theory, mathematics, sciences], anti-monotone function [order-theory, mathematics, sciences], antitone function [order-theory, mathematics, sciences], order-reversing function [order-theory, mathematics, sciences] Related terms: monotone, monotone operator, monotone transformation, monotonic, absolutely monotonic, strictly decreasing, strictly increasing, weakly decreasing, weakly increasing Translations (order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)): monotone Funktion [feminine] (German), monotona funkcija [feminine] (Serbo-Croatian), monoton fonksiyon (Turkish)
Disambiguation of 'order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)': 40 47 13

Inflected forms

Download JSON data for monotone function meaning in All languages combined (9.7kB)

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        "feminine"
      ],
      "word": "monotona funkcija"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "calculus: real function that either never decreases or never increases",
      "word": "monoton fonksiyon"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)",
      "tags": [
        "feminine"
      ],
      "word": "monotone Funktion"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)",
      "tags": [
        "feminine"
      ],
      "word": "monotona funkcija"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)",
      "word": "monoton fonksiyon"
    }
  ],
  "word": "monotone function"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.