## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

- noun The element of a set of numbers that when combined with another number in a particular operation leaves that number unchanged. For example, 0 is the identity element under addition for the real numbers, since if
*a*is any real number,*a*+ 0 = 0 +*a*=*a.*Similarly, 1 is the identity element under multiplication for the real numbers, since*a*× 1 = 1 ×*a*=*a.*

### from Wiktionary, Creative Commons Attribution/Share-Alike License.

- noun
*algebra*A member of a structure which, when applied to any other element via abinary operation induces anidentity mapping; more specifically, given an operation *, an element I is

### from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

- noun an operator that leaves unchanged the element on which it operates

## Etymologies

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## Examples

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