## additive inverse

### The opposite of a number. When added together, the sum is zero.

The additive inverse of a number a is the number that, when added to a, gives zero. More formally, given a number a, its additive inverse is denoted by -a, and satisfies the equation:

a + (-a) = 0

In other words, the additive inverse of a is the opposite of a, with the same magnitude. For example, the additive inverse of 3 is -3, since 3 + (-3) = 0. Similarly, the additive inverse of -5 is 5, since -5 + 5 = 0.

The concept of additive inverses is important in many areas of mathematics, including algebra, calculus, and linear algebra. In algebra, the concept is used to define the concept of a group, which is a set of elements together with a binary operation that satisfies certain properties, including the existence of an identity element and an inverse element for each element in the group. In calculus, the concept of additive inverses is used in the definition of limits, derivatives, and integrals. In linear algebra, the concept of additive inverses is used in the definition of vector spaces and in the study of matrices and systems of linear equations.

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