neutral element

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An element e is a neutral element for a binary operation ○ on a set S if, for all a in S, ae=ea=a. If the operation is called multiplication, a neutral element is normally called an identity element and may be denoted by 1. If the operation is called addition, such an element is normally denoted by 0, and is often called a zero element. However, there is a case for preferring the term ‘neutral element’, as there is an alternative definition for the term ‘zero element’ (see zero element).

Subjects: Mathematics.

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