URM Instructions are Countably Infinite

Theorem
The set $$\mathbb{I}$$ of all basic URM instructions is countably infinite.

Proof
We can immediately see that $$\mathbb{I}$$ is infinite as, for example, $$\phi: \N \to \mathbb{I}$$ defined as:
 * $$\phi \left({n}\right) = Z \left({n}\right)$$

is definitely injective.

From Unique Code for URM Instruction, we see that $$\beta: \mathbb{I} \to \N$$ is also an injection.

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