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 ?
Breast cancer is associated with dietary fat (which is associated with animal protein intake) and inversely with age at menarche (women who reach puberty at younger ages have a greater risk of breast cancer).
Fletcher's performance is inversely related to the number of questions he asks.
Rate of deposition is directly proportional to the square of the monomer concentration, and inversely proportional to the absolute temperature.
00 on wireless games, with reported spending inversely correlated with the purchaser's age.
Personal reported sun exposure was inversely associated with depression scores (p = 0.
Telomere length reflects biological age and is inversely associated with risk of cardiovascular disease (CVD).
BACKGROUND: Studies suggest that magnesium intake may be inversely related to risk of hypertension and type 2 diabetes mellitus and that higher intake of magnesium may decrease blood triglycerides and increase high-density lipoprotein (HDL) cholesterol levels.
Results: After adjustment for age, body mass index and lifestyle, as well as other dietary factors, soy protein intake was inversely associated with systolic BP as well as diastolic BP.
The incidence of non-Hodgkin's lymphoma (NHL) has increased in parallel with the incidence of cutaneous melanoma, and in Europe the incidence correlates inversely with latitude.
Volunteers' monobutyl phthalate concentrations were also inversely correlated with sperm motility.
These fluctuations scale inversely with the sensor size and, as the sensor dimensions shrink below 100 nm, can become the dominant source of noise.