Euler Phi Function of 1

Theorem

$\map \phi 1 = 1$

where $\phi$ denotes the Euler $\phi$ function.

Proof

The only (strictly) positive integer less than or equal to $1$ is $1$ itself.

By Integer is Coprime to 1, $1$ is coprime to itself.

Hence, by definition, there is exactly $1$ integer less than or equal to $1$ which is coprime with $1$.

Hence the result.

$\blacksquare$