inverse

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

2. Maths

a. another name for reciprocal

b. an inverse element

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

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inverse [′in‚vərs]

(mathematics)

The additive inverse of a real or complex numberais the number which when added toagives 0; the multiplicative inverse ofais the number which when multiplied withagives 1.

The inverse of a fractional idealIof an integral domainRis the set of all elementsxin the quotient fieldKofRsuch thatxyis inIfor allyinI.

For a setSwith a binary operationx·ythat has an identity elemente, the inverse of a member,x, ofSis another member,x̄, ofSfor whichx·x̄=x̄·x=e.

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(mathematics)

inverse - 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.