What is Identity element?
In [[mathematics]], the '''identity element''' (or '''neutral element''') of a [[set]] is a special element of that set. It is special because if it is combined with another element of that set, it does not change the other element. With [[addition]], the identity element is 0, because adding 0 to some [[number]] does not change the number. With [[multiplication]], it is 1. In a [[Group (mathematics)|group]] (an algebraic structure in mathematics), the identity element is sometimes denoted by the symbol <math>e</math>.<ref>{{Cite web|date=2020-03-25|title=Comprehensive List of Algebra Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/algebra-symbols/|access-date=2020-08-13|website=Math Vault|language=en-US}}</ref><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Identity Element|url=https://mathworld.wolfram.com/IdentityElement.html|access-date=2020-08-13|website=mathworld.wolfram.com|language=en}}</ref><ref>{{Cite web|title=Definition of IDENTITY ELEMENT|url=https://www.merriam-webster.com/dictionary/identity+element|access-date=2020-08-13|website=www.merriam-webster.com|language=en}}</ref> ==Further Examples== {| border=1, align=top !set!!operation!!identity |- |[[real number]]s||+ (addition)||[[Zero|0]] |- |[[real number]]s||• (multiplication)||[[1 (number)|1]] |- |[[real number]]s||''a<sup>b</sup>'' (exponentiation)||1 (right identity only) |- <!-- ||'''R'''<sup>''n''</sup> ||• (multiplication)|[[1 (number)|1]] --> |''m''-by-''n'' [[matrix (mathematics)|matrices]]|| + (addition)||[[zero matrix]] |- |''n''-by-''n'' square [[matrix (mathematics)|matrices]]|| • (multiplication)||[[identity matrix]] |- |all [[function (mathematics)|functions]] from a set ''M'' to itself||∘ (function composition)||[[identity map]] |- |[[character string]]s, lists|| concatenation || [[empty string]], empty list |- |[[extended real number]]s || minimum/infimum || +∞ |- |[[extended real number]]s || maximum/supremum || -∞ |- |subsets of a set ''M'' || ∩ (intersection) || ''M'' |- |sets || ∪ (union) || {} (empty set) |