Zero Element - Additive Identities

Additive Identities

An additive identity is the identity element in an additive group. It generalises the property 0 + x = x. Examples include:

• The null vector under vector addition
• The zero function or zero map, defined by z(x) = 0, under function addition, (f + g)(x) = f(x) + g(x), since z + f = f.
• The empty set under set union
• An empty sum or empty coproduct
• An initial object in a category (an empty coproduct, and so an identity under coproducts)