**Proposition**: Existence of Inverse Integers With Respect to Addition

For every integer \(x\in\mathbb Z\) there exists an **inverse integer** \(-x\in\mathbb Z\) such that the sum of both integers equals the integer zero:

\[x+(-x)=0.\]

| | | | | created: 2015-12-12 16:22:28 | modified: 2015-12-12 16:24:53 | by: *bookofproofs* | references: [696]

## 1.**Proof**: *(related to "Existence of Inverse Integers With Respect to Addition")*

(none)

[696] **Kramer Jürg, von Pippich, Anna-Maria**: “Von den natürlichen Zahlen zu den Quaternionen”, Springer-Spektrum, 2013

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