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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
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
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.
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.