Formal argument for why $(\mathbb{Z}/(4))_{(2)} = \mathbb{Z}/(4)$

Question

I'm learning about localizations, and I came across this statement: $$ \left(\mathbb{Z}/(4)\right)_{(2)} = \mathbb{Z}/(4) $$ Now, this statement makes sense because inverting all of the odd elements have no effect since the images of odd elements in $\mathbb{Z}/(4)$ are all invertible. But I'm struggling to write this down formally, what exactly can I write down to convince myself of this fact beyond a reasonable doubt?

Answer 1

The complement of $(2)$ is the set of all units of $\mathbb{Z}/(4)$.