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 ?
Finally, it is established that for any (but fixed) the inverse transversal S[degrees] of S, there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all amenable partial orders on S[degrees] and so every amenable partial order on S[degrees] is uniquely extended to an amenable partial order on S.
Suppose that (S, *) is a regular semigroup with an inverse transversal S[degrees].
According to Blyth and Almeida Santos in [5], if S is locally inverse, then
Suppose that S is a regular semigroup with an inverse transversal S[degrees].
Let S be a locally inverse semigroup with an inverse transversal S[degrees].
Suppose that S is a locally inverse semigroup with an inverse transversal S[degrees] If the partial order [less than or equal to] is an amenable partial order on S, then there exists an CS[degrees]-cone C such that [less than or equal to]c = [less than or equal to].
Effect between different sewing yarn and creep and inverse creep -before sewing process
The effect of creep before and inverse creep before sewing process were tabulated in the same way of above cases.
Table 5: Two-way ANOVA analysis of the Creep- before sewing and Inverse creep - before sewing process
0122 in between creep behavior (creep and Inverse creep before sewing process) this could be in highly significant difference.
The out put of the creep apparatus value are treated between the sewing material and extension length (Creep and Inverse creep after sewing process) was given in the table 6.
K, 1971, Generalized Inverse of Matrices and its applications, John Wiley and Sons, New York.