# inverse

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## inverse

**1.**

*Maths*

**a.**(of a relationship) containing two variables such that an increase in one results in a decrease in the other

**b.**(of an element) operating on a specified member of a set to produce the identity of the set:

*the additive inverse element of x is --x, the multiplicative inverse element of x is 1/x*

**3.**

*Logic*a categorial proposition derived from another by changing both the proposition and its subject from affirmative to negative, or vice versa, as

*all immortals are angels*from

*no mortals are angels*

## inverse

[′in‚vərs] (mathematics)

The additive inverse of a real or complex number

*a*is the number which when added to*a*gives 0; the multiplicative inverse of*a*is the number which when multiplied with*a*gives 1.The inverse of a fractional ideal

*I*of an integral domain*R*is the set of all elements*x*in the quotient field*K*of*R*such that*xy*is in*I*for all*y*in*I*.For a set

*S*with a binary operation*x*·*y*that has an identity element*e*, the inverse of a member,*x*, of*S*is another member,*x̄*, of*S*for which*x*·*x̄*=*x̄*·*x*=*e*.## inverse

(mathematics)Given a function, f : D -> C, a function g : C
-> D is called a left inverse for f if for all d in D, g (f d)
= d and a right inverse if, for all c in C, f (g c) = c and an
inverse if both conditions hold. Only an injection has a
left inverse, only a surjection has a right inverse and only
a bijection has inverses. The inverse of f is often written
as f with a -1 superscript.

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