inverse

Pronunciation

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Pronunciation

- (
*GA*) IPA: /ɪnˈvɝs/, /ˈɪnvɝs/

**inverse** (*not comparable*)

- Opposite in effect, nature or order.
- Reverse, opposite in order.
- (
*botany*) Inverted; having a position or mode of attachment the reverse of that which is usual. - (
*mathematics*) Having the properties of an**inverse**;*said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity*.*Multiplication is the***inverse**operation to division.

- (
*geometry*) That has the property of being an**inverse**(the result of a circle inversion of a given point or geometrical figure); that is constructed by circle inversion.*A circle inversion maps a given generalized circle to its***inverse**generalized circle.

- (
*category theory, of a category*) Whose every element has an**inverse**(morphism which is both a left inverse and a right inverse).

- Spanish: inverso

**inverse** (*plural* inverses)

- An inverted state: a state in which something has been turned (
*properly*) upside down or (*loosely*) inside out or backwards.*Cowgirl is the***inverse**of missionary.*321 is the***inverse**of 123.

- The result of an inversion,
*particularly*:- The reverse of any procedure or process.
*Uninstalling is the***inverse**of installation.

- (
*mathematics*) A ratio etc. in which the antecedents and consequents are switched.*The***inverse**of a:b is b:a.

- (
*geometry*) The result of a circle inversion; the set of all such points; the curve described by such a set.*The*P‘**inverse***of a point*P*is the point on a ray from the center*O*through*P*such that*OP*×*OP‘*=*r²*or the set of all such points.*

- (
*logic*) The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.*"Anything that isn't a dog doesn't go to heaven" is the***inverse**of "All dogs go to heaven." More generally, \lnot\mathsf{p}\to\lnot\mathsf{q} is the**inverse**of \mathsf{p}\to\mathsf{q} and is equivalent to the converse proposition \mathsf{q}\to\mathsf{p}.

**1896**, James Welton,*A Manual of Logic*, 2nd ed., Bk iii, Ch. iii, §102:- Inversion is the inferring, from a given proposition, another proposition whose subject is the contradictory of the subject of the original proposition. The given proposition is called the Invertend, that which is inferred from it is termed the
**Inverse**... The rule for Inversion is: Convert either the Obverted Converse or the Obverted Contrapositive.

- Inversion is the inferring, from a given proposition, another proposition whose subject is the contradictory of the subject of the original proposition. The given proposition is called the Invertend, that which is inferred from it is termed the

- The reverse of any procedure or process.
- (
*mathematics*) A second element which negates a first; in a binary operation, the element for which the binary operation—when applied to both it and an initially given element—yields the operation's identity element,*specifically:*- (
*addition*) The negative of a given number.*The additive***inverse**of x is -x, as x-x=0, as 0 is the additive identity element.

- (
*multiplication*) One divided by a given number.*The multiplicative***inverse**of x is x^{-1}, as x \times x^{-1}=1, as 1 the multiplicative identity element.

- (
*functions*) A second function which, when combined with the initially given function, yields as its output any term inputted into the first function.*The compositional***inverse**of a function f is f^{-1}, as f\ f^{-1}=\mathit{I}, as \mathit{I} is the identity function. That is, \forall x,f(f^{-1}(x))=\mathit{I}(x)=x.

- (
- (
*category theory*) A morphism which is both a left inverse and a right inverse. - (
*card games*) The winning of the coup in a game of rouge et noir by a card of a color different from that first dealt; the area of the table reserved for bets upon such an outcome.**1850**, Henry George Bohn,*The Hand-book of Games*, p. 343:- If the player... be determined to try his luck on the
**inverse**, he must place his money on a yellow circle, or rather a collection of circles, situated at the extremity of the table.

- If the player... be determined to try his luck on the
**1950**, Lawrence Hawkins Dawson,*Hoyle's Games Modernized*, 20th ed., p. 291:- The
*tailleur*never mentions the words ‘Black’ or ‘**Inverse**’, but always says that Red wins or Red loses, and that the colour wins or the colour loses.

- The

- (
*linguistics, Kiowa-Tanoan*) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

- (
*addition*) additive inverse - (
*multiplication*) multiplicative inverse - (
*composition*) compositional inverse - (
*geometry*) inverse point, inverse curve

**inverse** (inverses, *present participle* inversing; *past and past participle* inversed)

- compute (
*a point*).

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.006