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:
 * $\gcd \set {n, 1} = 1$

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

and so when $n = 1$ we have:
 * $\gcd \set {1, 0} = 1$