# Additive inverse

## Number that, when added to the original number, yields zero / From Wikipedia, the free encyclopedia

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In mathematics, the **additive inverse** of a number a is the number that, when added to a, yields zero. This number is also known as the **opposite** (number),[1] **sign change**,[2] and **negation**.[3] For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself.

The additive inverse of a is denoted by unary minus: −*a* (see also § Relation to subtraction below).[4] For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0.

Similarly, the additive inverse of *a* − *b* is −(*a* − *b*) which can be simplified to *b* − *a*. The additive inverse of 2*x* − 3 is 3 − 2*x*, because 2*x* − 3 + 3 − 2*x* = 0.[5]

The additive inverse is defined as its inverse element under the binary operation of addition (see also § Formal definition below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no net effect: −(−*x*) = *x*.