Additive inverse
Number that, when added to the original number, yields zero / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Negation (arithmetic)?
Summarize this article for a 10 year old
In mathematics, the additive inverse of a number a (sometimes called the opposite of a)[1] is the number that, when added to a, yields zero. The operation taking a number to its additive inverse is known as sign change[2] or negation.[3] For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself.
This article needs additional citations for verification. (January 2020) |
The additive inverse of a is denoted by unary minus: −a (see also § Relation to subtraction below).[4] 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.
Similarly, the additive inverse of a − b is −(a − b) which can be simplified to b − a. The additive inverse of 2x − 3 is 3 − 2x, because 2x − 3 + 3 − 2x = 0.[5]
The additive inverse is defined as its inverse element under the binary operation of addition (see also § Formal definition below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no net effect: −(−x) = x.