inverse
inverse
1. (converse) of a binary relation R. A derived relation R^{–1} such that whenever x R y then y R^{–1} x
where x and y are arbitrary elements of the set to which R applies. The inverse of “greater than” defined on integers is “less than”.
The inverse of a function f: X → Y
(if it exists) is another function, f^{–1}, such that f^{–1}: Y → X
and f(x) = y implies f^{–1}(y) = x
It is not necessary that a function has an inverse function.
Since for each monadic function f a relation R can be introduced such that R = {(x,y)  f(x) = y}
then the inverse relation can be defined as R^{–1} = {(y,x)  f(x) = y}
and this always exists. When f^{–1} exists (i.e. R^{–1} is itself a function) f is said to be invertible and f^{–1} is the inverse (or converse) function. Then, for all x, f^{–1}(f(x)) = x
To illustrate, if f is a function that maps each wife to her husband and g maps each husband to his wife, then f and g are inverses of one another.
2. See group.
3. of a conditional P→Q. The statement Q→P.
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"inverse." A Dictionary of Computing. . Encyclopedia.com. 18 Aug. 2017 <http://www.encyclopedia.com>.
"inverse." A Dictionary of Computing. . Encyclopedia.com. (August 18, 2017). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/inverse
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inverse
in·verse / ˈinvərs; inˈvərs/ • adj. opposite or contrary in position, direction, order, or effect: the wellobserved inverse relationship between disability and social contact. ∎ chiefly Math. produced from or related to something else by a process of inversion. • n. [usu. in sing.] something that is the opposite or reverse of something else: his approach is the inverse of most research on ethnic and racial groups. ∎ Math. a reciprocal quantity, mathematical expression, geometric figure, etc., that is the result of inversion. ∎ Math. an element that, when combined with a given element in an operation, produces the identity element for that operation. DERIVATIVES: in·verse·ly adv.
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"inverse." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 18 Aug. 2017 <http://www.encyclopedia.com>.
"inverse." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (August 18, 2017). http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/inverse
"inverse." The Oxford Pocket Dictionary of Current English. . Retrieved August 18, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/inverse
inverse
inverse adj. and sb. XVII. — L. inversus, pp. of invertere, f. IN1 + vertere turn.
So inversion XVI. invert vb. XVI. — L. invertere ‘turn in, turn outside in’, reverse.
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"inverse." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 18 Aug. 2017 <http://www.encyclopedia.com>.
"inverse." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. (August 18, 2017). http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/inverse0
"inverse." The Concise Oxford Dictionary of English Etymology. . Retrieved August 18, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionariesthesaurusespicturesandpressreleases/inverse0