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additive inverse
In mathematics, the additive inverse of a number is the number that, when added to , yields zero. This number is also known as the opposite (number),〔.〕 sign change, and negation.〔The term "negation" bears a reference to negative numbers, which can be misleading, because the additive inverse of a negative number is positive.〕 For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive. Zero is the additive inverse of itself.
The additive inverse of is denoted by unary minus: − (see the discussion below). 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 .
The additive inverse is defined as its inverse element under the binary operation of addition (see the discussion below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no effect: .
==Common examples==
For a number and, generally, in any ring, the additive inverse can be calculated using multiplication by −1; that is, . Examples of rings of numbers are integers, rational numbers, real numbers, and complex number.
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