inverse
adjective
- upside down or inverted
noun
- mathematical operation or function which undoes the effect of another entity of the same type
- opposite
Wiktionary
Pronunciation: /ɪnˈvɝs/ / /ˈɪnvɝs/
adj
Etymology: Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“against, in”) + vertere (“to turn”).
- Opposite in effect, nature or order.
- Reverse, opposite in order.
- Inverted; having a position or mode of attachment the reverse of that which is usual.
- 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.”
- 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.”
- Whose every element has an inverse (morphism which is both a left inverse and a right inverse).
noun
Etymology: Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“against, in”) + vertere (“to turn”).
- 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
“Uninstalling is the inverse of installation.”
- The result of an inversion
“The inverse of a:b is b:a.”
- The result of an inversion
“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.”
- The result of an inversion
“"Anything that isn't a dog doesn't go to heaven" is the inverse of "All dogs go to heaven." More generally, ¬ mathsf p→¬ mathsf q is the inverse of mathsf p→ mathsf q and is equivalent to the converse proposition mathsf q→ mathsf p.”
“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.”
- 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:
“The additive inverse of x is -x, as x-x=0, as 0 is the additive identity element.”
- 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:
“The multiplicative inverse of x is x⁻¹, as x×x⁻¹=1, as 1 the multiplicative identity element.”
- 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:
“The compositional inverse of a function f is f⁻¹, as ff⁻¹= mathit I, as mathit I is the identity function. That is, ∀x,f(f⁻¹(x))= mathit I(x)=x.”
- A morphism which is both a left inverse and a right inverse.
- 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.
“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.”
“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.”
- A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
verb
Etymology: Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“against, in”) + vertere (“to turn”).
- To compute the bearing and distance between two points.