Word Pronunciation & Dictionary

monotone function

Word Rarity Rare

Frequency: Zipf frequency 2.77 in modern English

Syllables: mono-tone -func-tion
IPA

23

Scrabble Score

16

Letters

4

Syllables

9

Unique Chars

Meaning

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).

noun

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).

noun

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.

Example Sentences

"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."
"Monotone functions on #91;a,b#93; have nice properties. For example, they are integrable on #91;a,b#93; 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 #92;mathit#123;BV#125;(#91;a,b#93;) contains the class of monotone functions on #91;a,b#93;."
"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)."

Inflected Forms

monotone functions (plural) monotonic function (alternative)

Phrases

monotone operator monotone transformation absolutely monotonic strictly decreasing strictly increasing weakly decreasing weakly increasing

Frequently Paired Words

monotone monotone operator monotone transformation monotonic absolutely monotonic strictly decreasing strictly increasing weakly decreasing

Synonyms

monotonic function

Questions

What does monotone function mean?: 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).

How to pronounce monotone function

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