Editing Random-access machine (section)

=== Finite vs unbounded ===
The definitional fact that any sort of counter machine without an unbounded register-"address" register must specify a register "r" by name indicates that the model requires "r" to be ''finite'', although it is "unbounded" in the sense that the model implies no upper limit to the number of registers necessary to do its job(s). For example, we do not require r < 83,617,563,821,029,283,746 nor r < 2^1,000,001, etc.

:Thus our model can "expand" the number of registers, if necessary to perform a certain computation. However this ''does'' mean that whatever number the model expands to must be ''finite''{{spaced ndash}}it must be indexable with a natural number: ''ω is not an option''.

We can escape this restriction by providing an unbounded register to provide the address of the register that specifies an indirect address.