"monotone function" meaning in English

See monotone function in All languages combined, or Wiktionary

Noun

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 Categories (other): Pages with 1 entry, Pages with entries, Terms with German translations, Terms with Turkish translations Disambiguation of Pages with 1 entry: 30 32 38 Disambiguation of Pages with entries: 31 31 38 Disambiguation of Terms with German translations: 32 34 33 Disambiguation of Terms with Turkish translations: 31 31 38 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': 76 13 11 Disambiguation of 'function that never increases as its independent variable increases': 77 12 11 Disambiguation of 'calculus: real function that either never decreases or never increases': 49 25 26
  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 Categories (other): Pages with 1 entry, Pages with entries, Terms with German translations, Terms with Turkish translations Disambiguation of Pages with 1 entry: 30 32 38 Disambiguation of Pages with entries: 31 31 38 Disambiguation of Terms with German translations: 32 34 33 Disambiguation of Terms with Turkish translations: 31 31 38 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, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with German translations, Terms with Serbo-Croatian translations, Terms with Turkish translations Disambiguation of English entries with incorrect language header: 31 30 40 Disambiguation of Entries with translation boxes: 30 31 39 Disambiguation of Pages with 1 entry: 30 32 38 Disambiguation of Pages with entries: 31 31 38 Disambiguation of Terms with German translations: 32 34 33 Disambiguation of Terms with Serbo-Croatian translations: 29 30 42 Disambiguation of Terms with Turkish translations: 31 31 38
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 46 14

Inflected forms

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          "text": "Section 1 contains Lebesgue's main tool, a theorem saying that monotone functions on the line are differentiable almost everywhere.",
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          "text": "Monotone functions on #x5B;a,b#x5D; have nice properties. For example, they are integrable on #x5B;a,b#x5D; and have only a countable number of jump discontinuities. In this section, we shall also show that every monotone function is a function of bounded variation, and hence the class #x5C;mathit#x7B;BV#x7D;(#x5B;a,b#x5D;) contains the class of monotone functions on #x5B;a,b#x5D;.",
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          "text": "We saw in the previous section that monotone functions have some nice properties. For example, a monotone function is continuous except possibly on a countable set. They are also closed under scalar multiplication, and the sum of two increasing functions is increasing. (Exercise (4) on page 103). However, the difference and product of two monotone functions are not necessarily monotone (Exercise (5) on page 103).",
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        ]
      ],
      "raw_glosses": [
        "(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)."
      ],
      "topics": [
        "calculus",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematical analysis"
      ],
      "glosses": [
        "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)."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "poset",
          "poset"
        ],
        [
          "partial order",
          "partial order"
        ]
      ],
      "raw_glosses": [
        "(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)."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "order-theory",
        "sciences"
      ]
    },
    {
      "glosses": [
        "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."
      ],
      "links": [
        [
          "Boolean function",
          "Boolean function"
        ]
      ],
      "qualifier": "Boolean algebra",
      "raw_glosses": [
        "(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."
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "function that either never decreases or never increases",
      "word": "monotonic function"
    },
    {
      "word": "monotonic function"
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "calculus: real function that either never decreases or never increases",
      "tags": [
        "feminine"
      ],
      "word": "monotone Funktion"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "calculus: real function that either never decreases or never increases",
      "tags": [
        "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"
}

Download raw JSONL data for monotone function meaning in English (7.9kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.

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