inverse

== English == === Etymology === Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“reverse, reciprocal”) + vertere (“to turn”). === Pronunciation === (General American) IPA(key): /ɪnˈvɝs/, /ˈɪnvɝs/ Rhymes: -ɜ(ɹ)s === Adjective === 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. (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. (category theory, of a category) Whose every element has an inverse (morphism which is both a left inverse and a right inverse). ==== Derived terms ==== ==== Related terms ==== ==== Translations ==== === Noun === inverse (plural inverses) An inverted state: a state in which something has been turned (properly) upside down or (loosely) inside out or backwards. 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 inverse P‘ 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, ¬ p → ¬ q {\displaystyle \lnot {\mathsf {p}}\to \lnot {\mathsf {q}}} is the inverse of p → q {\displaystyle {\mathsf {p}}\to {\mathsf {q}}} and is equivalent to the converse proposition q → p {\displaystyle {\mathsf {q}}\to {\mathsf {p}}} . (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 {\displaystyle x} is − x {\displaystyle -x} , as x − x = 0 {\displaystyle x-x=0} , as 0 {\displaystyle 0} is the additive identity element. (multiplication) One divided by a given number. The multiplicative inverse of x {\displaystyle x} is x − 1 {\displaystyle x^{-1}} , as x × x − 1 = 1 {\displaystyle x\times x^{-1}=1} , as 1 {\displaystyle 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 {\displaystyle f} is f − 1 {\displaystyle f^{-1}} , as f f − 1 = I {\displaystyle f\ f^{-1}={\mathit {I}}} , as I {\displaystyle {\mathit {I}}} is the identity function. That is, ∀ x , f ( f − 1 ( x ) ) = I ( x ) = x {\displaystyle \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. (linguistics, Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class. ==== Synonyms ==== (addition): additive inverse (multiplication): multiplicative inverse (composition): compositional inverse (geometry): inverse point, inverse curve ==== Derived terms ==== ==== Translations ==== ==== See also ==== (logic): obverse, converse, contraposition === Verb === inverse (third-person singular simple present inverses, present participle inversing, simple past and past participle inversed) (surveying) To compute the bearing and distance between two points. ==== Antonyms ==== compute (a point). ==== Derived terms ==== === Anagrams === Severin, enviers, inserve, veiners, venires, versine == Danish == === Adjective === inverse plural and definite singular attributive of invers == Dutch == === Pronunciation === Hyphenation: in‧ver‧se === Noun === inverse m or f by sense (plural inversen, no diminutive) inverse === Adjective === inverse inflection of invers: masculine/feminine singular attributive definite neuter singular attributive plural attributive === Anagrams === viseren == French == === Pronunciation === IPA(key): /ɛ̃.vɛʁs/ === Etymology 1 === From Latin inversus. ==== Adjective ==== inverse (plural inverses) inverse, the other way round ===== Derived terms ===== barre inverse dérivation inverse inversement ==== Noun ==== inverse m (plural inverses) the inverse, the contrary Synonyms: contraire, envers ===== Derived terms ===== === Etymology 2 === ==== Verb ==== inverse inflection of inverser: first/third-person singular present indicative/subjunctive second-person singular imperative === Further reading === “inverse”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012 === Anagrams === enivres, enivrés reviens Séverin vernies == German == === Pronunciation === === Adjective === inverse inflection of invers: strong/mixed nominative/accusative feminine singular strong nominative/accusative plural weak nominative all-gender singular weak accusative feminine/neuter singular == Italian == === Adjective === inverse feminine plural of inverso === Anagrams === svenire == Latin == === Participle === inverse vocative masculine singular of inversus