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.
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.
