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monotone function

monotone function noun: 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).

monotone function: a function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases...
Image: Oleg Alexandrov, Public domain, via Wikimedia Commons

Noun

monotone function (plural monotone functions)

  1. 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.
    • Section 1 contains Lebesgue's main tool, a theorem saying that monotone functions on the line are differentiable almost everywhere.2005, Anthony W. Knapp, Basic Real Analysis, Springer, page 357
  2. 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).
  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 function meaning in Tamil

monotone function in Tamil

ஒருபோக்குச் சார்பு

Examples of monotone function in a sentence

  • Monotone functions on #91;a,b#93; have nice properties.2011, Saminathan Ponnusamy, Foundations of Mathematical Analysis, Springer, page 469:
  • We saw in the previous section that monotone functions have some nice properties.2013, Donald Yau, A First Course in Analysis, World Scientific, page 104:

Synonyms of monotone function

Forms of monotone function

pluralmonotone functions
alternative formmonotonic function

Questions about monotone function

What does monotone function mean?
Monotone function means 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).
What is monotone function in Tamil?
Monotone function in Tamil is ஒருபோக்குச் சார்பு. See Monotone function meaning in Tamil.
How do you use monotone function in a sentence?
Monotone functions on #91;a,b#93; have nice properties.
What part of speech is monotone function?
Monotone function is a noun.
What is the plural of monotone function?
The plural of monotone function is monotone functions.

Words near monotone function in the dictionary

  1. monotonal
  2. monotonality
  3. monotonally
  4. monotone
  5. monotone convergence theorem
  6. monotone function
  7. monotone functions
  8. monotoned
  9. monotoneity
  10. monotonely
  11. monotones

Source and license

Adapted from Wiktionary: monotone function (page history and authors); monotone function (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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