The

**additive inverse**, or

**opposite**, of a number

*n*is the number which, when added to

*n*, yields zero. The additive inverse of

*n*is denoted -

*n*.

For example:

- The additive inverse of 7 is -7, because 7 + (-7) = 0;
- The additive inverse of -0.3 is 0.3, because -0.3 + 0.3 = 0.

The additive inverse of a number is its inverse element under the binary operation of addition.
It can be calculated using multiplication by -1; that is, -*n* = -1 × *n*.

Types of numbers with additive inverses include:

Types of numbers without additive inverses (of the same type) include: But note that we can construct the integers out of the natural numbers by formally including additive inverses. Thus we can say that natural numbers*do*have additive inverses, but because these additive inverses are not themselves natural numbers, the set of natural numbers is not

*closed*under taking additive inverses.

See also: Multiplicative inverse