URM Programs are Countably Infinite

Theorem
The set $$\mathbf{P}$$ of all URM programs is countably infinite.

Proof
We can immediately see that $$\mathbf{P}$$ is infinite as the number of URM instructions is infinite.

From Unique Code for URM Program, we see that $$\gamma: \mathbf{P} \to \N$$ is also an injection.

The result follows from Injection from Infinite to Countably Infinite Set‎.