# Opposite – Wikipedia, the free encyclopedia

In mathematics, the opposite (The symmetric for sum, The inverse additive) of a number

${displaystyle n,}$ is the number that, added with

${displaystyle n,}$ , gives zero. The additive inverse of

${displaystyle n,}$ is denoted

${displaystyle -n,}$ In our everyday language « opposite » would be equivalent to « opposite ».

Arithmetically, it can be calculated by multiplying by

${displaystyle -1,}$ , that is to say,

${displaystyle -n=-1times n}$ . Algebraically speaking, the opposite of an element of a group is its element symmetric with respect to the binary operation «

${displaystyle +,}$ « (when using additive notation).

For example:

• The opposite of
${displaystyle 8,}$ is

${displaystyle -8,}$ , because

${displaystyle 8+(-8)=0,}$ ;

• The opposite of
${displaystyle -0,3,}$ is

${displaystyle 0,3,}$ , because

${displaystyle -0,3+0,3=0,}$ .

So, for the example above,

${displaystyle -(-0,3)=0,3,}$ .

Sets of numbers in which each element has opposites:

Sets of numbers without opposites:

Note that the integers are constructed from the natural numbers to which the opposites are formally added.