inverse
Language: English
Part of speech: noun
Pronunciation: ipa: /ɪnˈvɝs/
ipa: /ˈɪnvɝs/
rhymes: -ɜ(ɹ)s
Forms: form: inverses
Etymology: Recorded since 1440, from Latin inversus, the past participle of invertere (“to invert”), itself from in- (“in, on”) + vertere (“to turn”).
Senses: examples: text: Cowgirl is the inverse of missionary.
text: 321 is the inverse of 123.
glosses: An inverted state: a state in which something has been turned (properly) upside down or (loosely) inside out or backwards.
examples: Uninstalling is the inverse of installation.
glosses: The result of an inversion
The reverse of any procedure or process.
examples: The inverse of a:b is b:a.
topics: mathematics
sciences
glosses: The result of an inversion
A ratio etc. in which the antecedents and consequents are switched.
examples: 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.
topics: geometry
mathematics
sciences
glosses: The result of an inversion
The result of a circle inversion; the set of all such points; the curve described by such a set.
examples: text: "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.
text: 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.
ref: 1896, James Welton, A Manual of Logic, 2nd edition, Bk iii, Ch. iii, §102:
topics: human-sciences
logic
mathematics
philosophy
sciences
glosses: The result of an inversion
The non-truth-preserving proposition constructed by negating both the premise and conclusion of an initially given proposition.
examples: The additive inverse of x is -x, as x-x=0, as 0 is the additive identity element.
topics: mathematics
sciences
glosses: 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 negative of a given number.
qualifier: addition
examples: The multiplicative inverse of x is x⁻¹, as x×x⁻¹=1, as 1 the multiplicative identity element.
topics: mathematics
sciences
glosses: 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:
One divided by a given number.
qualifier: multiplication
examples: 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.
topics: mathematics
sciences
glosses: 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:
A second function which, when combined with the initially given function, yields as its output any term inputted into the first function.
qualifier: functions
topics: category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: A morphism which is both a left inverse and a right inverse.
examples: text: 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.
ref: 1850, Henry George Bohn, The Hand-book of Games, page 343:
text: 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.
ref: 1950, Lawrence Hawkins Dawson, Hoyle's Games Modernized, 20th edition, page 291:
topics: card-games
games
glosses: 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.
topics: human-sciences
linguistics
sciences
glosses: A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
Synonyms: sense: addition
word: additive inverse
sense: multiplication
word: multiplicative inverse
word: compositional inverse
topics: geometry
mathematics
sciences
word: inverse point
topics: geometry
mathematics
sciences
word: inverse curve
Derived terms: coinverse
pseudoinverse
Related terms: topics: logic
mathematics
philosophy
human-sciences
sciences
word: obverse
topics: logic
mathematics
philosophy
human-sciences
sciences
word: converse
topics: logic
mathematics
philosophy
human-sciences
sciences
word: contraposition