Editing Identity element (section)

{{Short description|Specific element of an algebraic structure}}
In [[mathematics]], an '''identity element''' or '''neutral element''' of a [[binary operation]] is an element that leaves unchanged every element when the operation is applied.<ref>{{Cite web |url = http://mathworld.wolfram.com/IdentityElement.html |title = Identity Element |last = Weisstein |first = Eric W. |authorlink = Eric W. Weisstein|website = mathworld.wolfram.com |language = en |access-date = 2019-12-01 }}</ref><ref>{{Cite web |url = https://www.merriam-webster.com/dictionary/identity+element |title = Definition of IDENTITY ELEMENT |website = www.merriam-webster.com |access-date = 2019-12-01 }}</ref> For example, 0 is an identity element of the [[addition]] of [[real number]]s. This concept is used in [[algebraic structure]]s such as [[group (mathematics)|group]]s and [[ring (mathematics)|ring]]s. The term ''identity element'' is often shortened to ''identity'' (as in the case of additive identity and multiplicative identity)<ref name=":0">{{Cite web |url = https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/identity-element |title = Identity Element |website = www.encyclopedia.com |access-date = 2019-12-01}}</ref> when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.