Search results
Results from the WOW.Com Content Network
In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [11] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [12]
An involution is a function f : X → X that, when applied twice, brings one back to the starting point. In mathematics, an involution, involutory function, or self-inverse function [1] is a function f that is its own inverse, f(f(x)) = x. for all x in the domain of f. [2] Equivalently, applying f twice produces the original value.
Sometimes, the inverse of a function cannot be expressed by a closed-form formula. For example, if f is the function = , then f is a bijection, and therefore possesses an inverse function f −1. The formula for this inverse has an expression as an infinite sum:
The addition of vectors is commutative, ... This property leads to two different "inverse" operations of ... For example, if the function f is defined as ...
Under addition, a ring is an abelian group, which means that addition is commutative and associative; it has an identity, called the additive identity, and denoted 0; and every element x has an inverse, called its additive inverse and denoted −x. Because of commutativity, the concepts of left and right inverses are meaningless since they do ...
Subtraction is itself a sort of inverse to addition, in that adding x and subtracting x are inverse functions. Given a set with an addition operation, one cannot always define a corresponding subtraction operation on that set; the set of natural numbers is a simple example.
That the function g is injective implies that given some equality of the form a ∗ x = b, where the only unknown is x, there is only one possible value of x satisfying the equality. More precisely, we are able to define some function f, the inverse of g, such that for all x f(g(x)) = f(a ∗ x) = x.
The inverse of addition is subtraction, and the inverse of multiplication is division. Similarly, a logarithm is the inverse operation of exponentiation . Exponentiation is when a number b , the base , is raised to a certain power y , the exponent , to give a value x ; this is denoted b y = x . {\displaystyle b^{y}=x.}