Concept

Additive identity

Résumé
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 set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings. Elementary examples
  • The additive identity familiar from elementary mathematics is zero, denoted 0. For example, *:5+0 = 5 = 0+5.
  • In the natural numbers \N (if 0 is included), the integers \Z, the rational numbers \Q, the real numbers \R, and the complex numbers \C, the additive identity is 0. This says that for a number n belonging to any of these sets, *:n+0 = n = 0+n.
Formal definition Let N be a group that is closed under the operation of addition, denoted +. An additive identity for N, denoted
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