## Quick Reference

Suppose that, for the binary operation ○ on the set *S*, there is a neutral element *e*. An element *a*′ is an inverse (or inverse element) of the element *a* if *a* ○ *a*′=*a*′○ *a*=*e*. If the operation is called multiplication, the neutral element is normally called the identity element and may be denoted by 1. Then the inverse *a*′ may be called a multiplicative inverse of *a* and be denoted by *a*^{−1}, so that *aa*^{−1}=*a*^{−1}*a*=1 (or *e*). If the operation is addition, the neutral element is denoted by 0, and the inverse *a*′ may be called an additive inverse (or a negative) of *a* and be denoted by −*a*, so that *a*+(−*a*)=(−*a*)+*a*=0. See also group.

*Subjects:*
Mathematics.

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