In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the...

In mathematics, the additive inverse of an element x, denoted -x, is the element that when added to x, yields the additive identity, 0. In the most familiar...

two-sided identity, or simply an identity. An identity with respect to addition is called an additive identity (often denoted as 0) and an identity with respect...

to the same thing, depending on the context. An additive identity is the identity element in an additive group or monoid. It corresponds to the element...

(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...

leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers...

The identity also links five fundamental mathematical constants: The number 0, the additive identity The number 1, the multiplicative identity The number...

of 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...

b = b ⋅ a. Additive and multiplicative identity: there exist two distinct elements 0 and 1 in F such that a + 0 = a and a ⋅ 1 = a. Additive inverses: for...

proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are used in the article...