Additive inverse

In mathematics, the additive inverse of an <a href="/facts/Element_(mathematics)/Q2mx1vHL">element</a> x, denoted −x, is the element that when <a href="/facts/Addition/apFWJBFB">added</a> to x, yields the <a href="/facts/Additive_identity/wNDDkXJe">additive identity</a>, <a href="/facts/0/4NBRtKHc">0 (zero)</a>. In the most familiar cases, this is the <a href="/facts/Number/auQSAE2m">number</a> 0, but it can also refer to a more generalized <a href="/facts/Zero_element/PvH2qhxh">zero element</a>.
In <a href="/facts/Elementary_mathematics/J0Jt18pb">elementary mathematics</a>, the additive inverse is often referred to as the opposite number, or its negative. The <a href="/facts/Unary_operation/kb6CkgsX">unary operation</a> of arithmetic negation is closely related to <a href="/facts/Subtraction/dEUrp6k0">subtraction</a> and is important in <a href="/facts/Elementary_algebra/973nufT7">solving algebraic equations</a>. Not all <a href="/facts/Set_(mathematics)/BfucfHMq">sets</a> where addition is defined have an additive inverse, such as the <a href="/facts/Natural_number/u65og8JE">natural numbers</a>.

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Additive inverse