Inverse Completion of Natural Numbers
From ProofWiki
Theorem
There exists an inverse completion of the natural numbers under addition.
Proof
The set of natural numbers under addition can be denoted $\left ({\N, +}\right)$.
From Natural Numbers under Addition is Commutative Monoid, the algebraic structure $\left ({\N, +}\right)$ is a commutative monoid (and therefore a commutative semigroup) all of whose elements are cancellable.
The result follows from the Inverse Completion Theorem.
$\blacksquare$
