# Online Encyclopedia

# Additive inverse

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.

Thus by the last example, −(−0.3) = 0.3.

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.