mathematics, the additive inverse of an element x, denoted −x, is the element that when added to x, yields the additive identity. This additive identity is...

added for specifying the operation, such as in additive inverse, multiplicative inverse, and functional inverse. In this case (associative operation), an invertible...

omitted and then tacitly understood (in contrast to the additive inverse). Multiplicative inverses can be defined over many mathematical domains as well...

inequality relation would be reversed. The rules for the additive inverse, and the multiplicative inverse for positive numbers, are both examples of applying...

(negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative...

numbers. This includes the existence of an additive inverse −a for each element a and of a multiplicative inverse b−1 for each nonzero element b. This allows...

phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted...

construction. The additive inverse of a number is unique, as is shown by the following proof. As mentioned above, an additive inverse of a number is defined...

is given below. An additive category may then be defined as a semiadditive category in which every morphism has an additive inverse. This then gives the...

addition operation Additive set-function see Sigma additivity Additive category, a preadditive category with finite biproducts Additive inverse, an arithmetic...

(that is, 0 is the additive identity). For each a in R there exists −a in R such that a + (−a) = 0 (that is, −a is the additive inverse of a). R is a monoid...

axioms that define a ring; they are the additive identity (0), the multiplicative identity (1), and the additive inverse of 1 (−1). The arithmetic operations...

of rings, dropping the requirement that each element must have an additive inverse. At the same time, semirings are a generalization of bounded distributive...

− 3 = 2. Subtraction is the inverse of addition. The function whose value for any real or complex argument is the additive inverse of that argument. For example...

is therefore shown. 0 (number) Additive inverse Identity element Multiplicative identity Weisstein, Eric W. "Additive Identity". mathworld.wolfram.com...

of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers...

conditional sentence Additive inverse, the inverse of a number that, when added to the original number, yields zero Compositional inverse, a function that...

(for all numbers x), the square of x is the same as the square of its additive inverse −x. That is, the square function satisfies the identity x2 = (−x)2...

unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is...

operations needed to perform calculations. The additive identity element is 0 and the additive inverse of a number is the negative of that number. For...

{\displaystyle a\times 1=a} for every real number a. Every real number a has an additive inverse denoted − a . {\displaystyle -a.} This means that a + ( − a ) = 0 {\displaystyle...

its additive inverse −1 are always units. More generally, any root of unity in a ring R is a unit: if rn = 1, then rn−1 is a multiplicative inverse of...

gives the additive inverse: (−1)v = −v. Here, + is addition either in the field or in the vector space, as appropriate; and 0 is the additive identity...

Replacing i by −i, j by −j, and k by −k sends a vector to its additive inverse, so the additive inverse of a vector is the same as its conjugate as a quaternion...

numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called complements. Thus subtraction...

Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are inverse problems: given the size...

operations are associative and commutative. Each nimber is its own additive inverse. In particular for some pairs of ordinals, their nimber sum is smaller...

additive semigroup of positive natural numbers. Absorbing element Additive inverse Generalized inverse Identity (equation) Identity function Inverse element...

determines an addition operation, an additive inverse operation, and an additive identity; for this reason, an additive group can be described as a set that...

Additive synthesis example A bell-like sound generated by additive synthesis of 21 inharmonic partials Problems playing this file? See media help. Additive...