Encyclopedia > Additive inverse

  Article Content

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.

See also: Multiplicative inverse

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
BBC News 24

... signals, and this is seen by some as influential (to a certain limited extent) in promoting the take-up of digital television. BBC News 24 broadcasts from the BBC ...

This page was created in 24.5 ms