[Dylan16807]

In a theoretical sense, an unbounded number is always finite.

In a practical sense, turing machines don't voraciously consume tape. Adding extra feet of tape gives you an exponential increase in what you can compute. So if you set up a program to be reasonably judicious with its tape use, you can just say that if it reaches an end you pause it for a day, head to the shop, and buy another reel. Big computations take a lot of time anyway.

[hardlianotion]

Any given number is always bounded. I am not sure it makes sense to talk about an unbounded number

[Dylan16807]

The size number of the unbounded tape size is always finite, is that better?