Integer is Coprime to 1

Theorem
Every integer is coprime to $$1$$.

That is:
 * $$\forall n \in \Z: n \perp 1$$

Proof
Follows from the definitions of coprime and greatest common divisor as follows.

When $$n \in \Z: n \ne 0$$ we have:
 * $$\gcd \left\{{n, 1}\right\} = 1$$

Then by definition again:
 * $$\gcd \left\{{n, 0}\right\} = n$$

and so when $$n = 1$$ we have $$\gcd \left\{{1, 0}\right\} = 1$$.