[leroy-is-here]

To your point, Turing's paper 'On Computable Numbers' doesn't even mention the length of the tape. He doesn't specify that it must be infinite at all.

[eesmith]

While the paper does not explicitly state it, he shows that π and e are computable. Those cannot be expressed on a fixed-length tape.

There is also a demonstration why an infinite number of symbols does not give more computability over a finite number of symbols. I believe this only makes sense if the tape length is infinite.

[leroy-is-here]

Yeah, the model only makes sense with an infinite length tape. I only mention it because many commenters get stuck on the word 'infinite' without realizing how inconsequential it is.

[schoen]

I'm surprised to see that, but all subsequent authors have required it to be infinite (as a condition to distinguish it from other models of computation), and Turing himself later referred to it as infinite:

https://en.wikipedia.org/wiki/Turing_machine#Physical_descri...