Additive inverse

The additive inverse of a number is the number which sums to $0$ with the other number.

If we have: \[a + b = 0,\]

we can say that $b = -a.$ Thus, $b$ is the additive inverse of $a.$

Examples include $3$ and $-3$ or $0.5$ and $-0.5.$

Overview

In mathematics, the additive inverse of a number $a$ is the number that, when added to $a$, yields zero. This operation is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the opposite of a positive number is negative, and the opposite of a negative number is positive. Zero is the additive inverse of itself.

The additive inverse of $a$ is denoted by unary minus: $-a$. 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, which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, the double additive inverse has no effect: $-( -x ) = x.$

This article is a stub. Help us out by expanding it.