Definify.com
Webster 1913 Edition
Inverse
1.
Opposite in order, relation, or effect; reversed; inverted; reciprocal; – opposed to
direct
. 2.
(Bot.)
Inverted; having a position or mode of attachment the reverse of that which is usual.
3.
(Math.)
Opposite in nature and effect; – said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity;
as, multiplication is the
. The symbol of an inverse operation is the symbol of the direct operation with inverse
operation to division1
as an index. Thus
sin
means the arc or angle whose sine is x. 1
x
Inverse figures
(Geom.)
, two figures, such that each point of either figure is inverse to a corresponding point in the order figure.
– Inverse points
(Geom.)
, two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius.
– Inverse ratio
, or
Reciprocal ratio
(Math.)
, the ratio of the reciprocals of two quantities.
– Inverse proportion
, or Reciprocal proportion
an equality between a direct ratio and a reciprocal ratio; thus,
4 : 2 : : ⅓ : ^{1}⁄_{6}
, or 4 : 2 : : 3 : 6, inversely.In′verse
,Noun.
That which is inverse.
Thus the course of human study is the
inverse
of the course of things in nature. Tatham.
Webster 1828 Edition
Inverse
INVERSE
,Adj.
Inverted; reciprocal. Inverse proportion or ratio, is when the effect or result of any operation is less in proportion as the cause is greater, or is greater in proportion as the cause is less. Thus the time in which a quantity of work may be performed, will be less in proportion as the number of workmen is greater, and greater in proportion as the number of workmen is less. If ten men can perform a certain quantity of work in six days,then twenty men will perform the same work in three days. Inverse proportion is opposed to direct.
Definition 2024
inverse
inverse
See also: inversé
English
Adjective
inverse (not comparable)
 Inverted in its various senses, including:
 (properly) Upside down.
 The rarity of the inverse Flying Jenny made it highly valuable.
 (figuratively) Reverse: opposite in order, nature, or effect.
 Mutually exclusive to a given, beginning when it ceases and vice versa.
 (mathematics) Mutually negating: having the property of producing an output identical to the input of a given operation.
 Multiplication is the inverse operation to division.
 (mathematics) Opposite in nature or effect.
 A ratio is said to be inverse when one term increases in exact proportion as the other decreases or vice versa.
 (geometry) Related to an initial point, line, &c. through circle inversion.
 (mineralogy) Having certain reversed crystalline structures.
 (botany) Having a position or mode of attachment reversed from the normal arrangement.
 (properly) Upside down.
Derived terms
 inverse function
 inverse image
 inverse spelling
 inversely
Related terms
Translations
upside down — see upside down
opposite in effect or nature


(mathematics) having the properties of an inverse
Noun
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 &c. 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 such that OP × OP‘ = r² or the set of all such points.
 (logic) The nontruthpreserving 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, is the inverse of and is equivalent to the converse proposition .

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.
 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 is , as , as is the additive identity element.
 (multiplication) One divided by a given number.
 The multiplicative inverse of is , as , as 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 is , as , as is the identity function. That is, .
 (addition) The negative of a given number.
 (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 Handbook 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.
 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.
 1850, Henry George Bohn, The Handbook of Games, p. 343:
 (linguistics, KiowaTanoan) 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
See also
 (logic): obverse, converse, contraposition
Translations
opposite of a given due to contrary effects or nature

reverse procedure


math: element

logic: statement

Verb
inverse (thirdperson singular simple present inverses, present participle inversing, simple past and past participle inversed)
Antonyms
 compute (a point).
Anagrams
Dutch
Pronunciation
 Hyphenation: in‧ver‧se
Noun
inverse m, f (plural inversen)
Adjective
inverse
 Inflected form of invers
Anagrams
French
Pronunciation
Adjective
inverse m, f (plural inverses)
 inverse, the other way round.
Noun
inverse m (plural inverses)
Synonyms
Verb
inverse
 firstperson singular present indicative of inverser
 thirdperson singular present indicative of inverser
 firstperson singular present subjunctive of inverser
 thirdperson singular present subjunctive of inverser
 secondperson singular imperative of inverser