**identity**

**identity element:**

an element (such as 0 in the set of all integers under addition or 1 in the set of positive integers under multiplication) that leaves any element of the set to which it belongs unchanged when combined with it by a specified operation.

**inverse**:

(of an element) operating on a specified member of a set to produce the identity of the set:

the additive inverse element of x is –x, the multiplicative inverse element of x is 1/x.

Origin:

First recorded in 1560–70; from Late Latin identitās, equivalent to Latin ident(idem) “repeatedly, again and again,” earlier unattested idem et idem (idem neuter of īdem “the same” + et “and”) + -itās noun suffix; see -ity. British dictionary: C16: from Late Latin identitās, from Latin idem the same. —Dictionary.com. //

First Known Use of identity: 1545. History and Etymology for identity: Middle French identité, from Late Latin identitat-, identitas, probably from Latin identidem repeatedly, contraction of idem et idem, literally, same and same. —Merriam-Webster.

See historical usage note at Dictionary.com.*

Sources: 1, 2.

Updated: 23 September 2020 {4:42 PM}