zero element

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An element z is a zero element for a binary operation ○ on a set S if, for all a in S, az=za=z. Thus the real number 0 is a zero element for multiplication since, for all a, a0=0a=0. The term ‘zero element’, also denoted by 0, may be used for an element such that a+0=0+a=a for all a in S, when S is a set with a binary operation+called addition. Strictly speaking, this is a neutral element for the operation+.

Subjects: Mathematics.

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