In mathematics, the additive inverse of an element x, denoted -x[1], is the element that when added to x, yields the additive identity, 0[2]. In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element.
In elementary mathematics, the additive inverse is often referred to as the opposite number[3][4]. The concept is closely related to subtraction[5] and is important in solving algebraic equations[6]. Not all sets where addition is defined have an additive inverse, such as the natural numbers[7].