Natural Number Addition is Commutative/Proof 1
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Theorem
The operation of addition on the set of natural numbers $\N$ is commutative:
- $\forall m, n \in \N: m + n = n + m$
Proof
Consider the natural numbers defined as a naturally ordered semigroup.
By definition, the operation in a naturally ordered semigroup is commutative.
Hence the result.
$\blacksquare$