# 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
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

## 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, , of S for which x · = · 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.
References in periodicals archive ?
Colorectal cancers are consistently inversely associated with in-takes of 14 different dietary fiber fractions (although only one is statistically significant).
Gallinarum cases were inversely related to the numbers of human S.
Silicone and HNBR test samples show volume swell inversely proportional to percent of methanol concentration, while swell is proportional to percent of methanol concentration on the FKM test samples.
These fluctuations scale inversely with the sensor size and, as the sensor dimensions shrink below 100 nm, can become the dominant source of noise.
Here's news from the research front--vacations are inversely correlated with mortality--take more, live longer.
25 for a bond with a \$1,000 face value, and its yield, which moves inversely to price, dropped to 6.
A taxpayer has diminished its risk of loss if changes in the stock's FMV and the position with respect to substantially similar or related property are reasonably expected to vary inversely.
MnH was inversely associated with Verbal IQ, Performance IQ, and Total Scale IQ, but MnB was not significantly associated with Total Scale or Verbal IQ.
The strength of a woman's EMFs exposure weakly correlated inversely with her concentrations of urinary 6-OHMS, Davis' team found.
The degree of atherosclerotic build up in the arteries of these subjects was inversely correlated with the amount of tea consumed.

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