[thrown123098]

Wrong: https://en.wikipedia.org/wiki/Arbitrarily_large

[rrobukef]

There is a physical limit to the number of disks you can add to your CPU. There is a physical limit to the memory you can address in your CPU (48-bits). It is not arbitrarily large.

Also wrong for Turing Machines, it really is infinite. That's a big difference to arbitrarily large. The halting problem is undecidable for TM's but not for arbitrarily large (you'll need precise definitions though).

[thrown123098]

It is left as an exercise to the reader to find a natural number which isn't arbitrarily large but calculable.