In mathematics, the additive inverse of a number a (sometimes called the opposite of a) is the number that, when added to a, yields zero. The operation...

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

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

numbers, including the existence of an additive inverse −a for all elements a, and of a multiplicative inverse b−1 for every nonzero element b. This allows...

(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...

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

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

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

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...

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

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

natural numbers: the integers, by including an additive identity 0 (if not yet in) and an additive inverse −n for each nonzero natural number n; the rational...

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

= 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...

(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...

{\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...

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...

(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...

mathematics, −1 is the additive inverse of 1. −1, minus one, or negative one may also refer to: the exponent −1 denoting a multiplicative inverse the superscript...

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

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 a ring, dropping the requirement that each element must have an additive inverse. At the same time, it is a generalization of bounded distributive lattices...

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...

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...

idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the semiring is compensated somewhat by the idempotent rule A ⊕...

Note that steps 2 and 3 together are a valid method to compute the additive inverse − n {\displaystyle -n} of any (positive or negative) integer n {\displaystyle...

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...

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

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...

ones" number (the term "complement" refers to such pairs of mutually additive inverse numbers, here in respect to a non-0 base number). This mathematical...