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Webster 1913 Edition

Inverse

In-verse′

Adj.

[L.

inversus

, p. p. of

invertere

: cf. F.

inverse

. See

Invert

Opposite in order, relation, or effect; reversed; inverted; reciprocal; – opposed to

direct

(Bot.)

Inverted; having a position or mode of attachment the reverse of that which is usual.

(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

inverse

operation to division

. The symbol of an inverse operation is the symbol of the direct operation with

-1

as an index. Thus

sin

-1

means the arc or angle whose sine is 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&frasl;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.

invers'. [L. inversus. See Invert.]

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

See also: inversé

English

Adjective

A chart depicting the strong inverse relationship between prosperity and fertility in existing societies

inverse ‎(not comparable)

Inverted in its various senses, including:
1. (properly) Upside down.
  The rarity of the inverse Flying Jenny made it highly valuable.
2. (figuratively) Reverse: opposite in order, nature, or effect.
3. Mutually exclusive to a given, beginning when it ceases and vice versa.
4. (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.
5. (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.
6. (geometry) Related to an initial point, line, &c. through circle inversion.
7. (mineralogy) Having certain reversed crystalline structures.
8. (botany) Having a position or mode of attachment reversed from the normal arrangement.

Derived terms

Related terms

Translations

upside down — see upside down

opposite in effect or nature

Catalan: invers (ca)
Dutch: tegengesteld (nl), tegenovergesteld (nl)

German: entgegengesetzt
Spanish: inverso (es) m

reverse, opposite in order

Catalan: invers (ca)
Dutch: omgekeerd (nl)

German: umgekehrt (de)

(mathematics) having the properties of an inverse

Catalan: invers (ca)
Dutch: invers (nl)

Spanish: inverso (es) m
Swedish: invers (sv) c

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:
1. The reverse of any procedure or process.
  Uninstalling is the inverse of installation.
2. (mathematics) A ratio &c. in which the antecedents and consequents are switched.
  The inverse of a:b is b:a.
3. (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.
4. (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.
(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:
1. (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.
2. (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.
3. (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, $\forall x,f^{-1}(f(x))={\mathit {I}}(x)=x$ .
(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.
- 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.
(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

Translations

opposite of a given due to contrary effects or nature

Dutch: tegendeel (nl) n, tegengestelde (nl) n, tegenovergestelde (nl) n

reverse procedure

Dutch: omgekeerde (nl) n, spiegelbeeld (nl) n
Finnish: käänteinen (fi) toimenpide (fi)

Trió: da

math: element

Dutch: inverse (nl) c

Finnish: käänteisarvo (fi)

logic: statement

Finnish: käänteislause

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).

Anagrams

versine