VS.

# Inverse vs. Reciprocal

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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).

• Inverse (noun)

An inverted state: a state in which something has been turned upside down or inside out or backwards.

"Cowgirl is the inverse of missionary."

"321 is the inverse of 123."

• Inverse (noun)

The result of an inversion, particularly:

• Inverse (noun)

The reverse of any procedure or process.

"Uninstalling is the inverse of installation."

• Inverse (noun)

A ratio etc. in which the antecedents and consequents are switched.

"The inverse of a:b is b:a."

• Inverse (noun)

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."

• Inverse (noun)

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:

• Inverse (noun)

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, $\lnot\mathsf\left\{p\right\}\to\lnot\mathsf\left\{q\right\}$ is the inverse of $\mathsf\left\{p\right\}\to\mathsf\left\{q\right\}$ and is equivalent to the converse proposition $\mathsf\left\{q\right\}\to\mathsf\left\{p\right\}$."

• Inverse (noun)

The negative of a given number.

"The additive inverse of $x$ is $-x$, as $x-x=0$, as $0$ is the additive identity element."

• Inverse (noun)

One divided by a given number.

"The multiplicative inverse of $x$ is $x^\left\{-1\right\}$, as $x \times x^\left\{-1\right\}=1$, as $1$ the multiplicative identity element."

• Inverse (noun)

A morphism which is both a left inverse and a right inverse.

• Inverse (noun)

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.

• Inverse (noun)

A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

• Inverse (verb)

To compute the bearing and distance between two points.

Of a feeling, action or such: mutual, uniformly felt or done by each party towards the other or others; two-way.

"reciprocal love; reciprocal duties"

Mutually interchangeable.

expressing mutual action, applied to pronouns and verbs; also in a broad sense: reflexive

Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.

Done, given, felt, or owed in return

"a reciprocal invitation to lunch"

• Reciprocal (noun)

The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.

"0.5 is the reciprocal of 2."

• Reciprocal (noun)

A construction expressing mutual action.

Wiktionary

Opposite in order, relation, or effect; reversed; inverted; reciprocal; - opposed to direct.

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

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 x means the arc or angle whose sine is x.

• Inverse (noun)

That which is inverse.

Recurring in vicissitude; alternate.

Done by each to the other; interchanging or interchanged; given and received; due from each to each; mutual; as, reciprocal love; reciprocal duties.

Mutually interchangeable.

Reflexive; - applied to pronouns and verbs, but sometimes limited to such pronouns as express mutual action.

Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities. See the Phrases below.

• Reciprocal (noun)

That which is reciprocal to another thing.

• Reciprocal (noun)

The quotient arising from dividing unity by any quantity; thus ¼ is the reciprocal of 4; 1/(a + b) is the reciprocal of a + b. The reciprocal of a fraction is the fraction inverted, or the denominator divided by the numerator.

Webster Dictionary
• Inverse (noun)

something inverted in sequence or character or effect;

"when the direct approach failed he tried the inverse"

reversed (turned backward) in order or nature or effect

opposite in nature or effect or relation to another quantity ;

"a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)"

• Reciprocal (noun)

something (a term or expression or concept) that has a reciprocal relation to something else;

"risk is the reciprocal of safety"

• Reciprocal (noun)

(mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7

• Reciprocal (noun)

hybridization involving a pair of crosses that reverse the sexes associated with each genotype

concerning each of two or more persons or things; especially given or done in return;

"reciprocal aid"

"mutual respect"

"reciprocal privileges at other clubs"

of or relating to or suggestive of complementation;

"interchangeable electric outlets"