[jasamer]

Touring completeness is about accurately simulating any Turing machine. Not approximately simulating one (what would that even mean?), or simulating just some of them.

When we say something is Turing complete, there’s always an implicit “if it ran on a computer with unlimited memory” assumption that comes with it, because no computer with limited memory can ever simulate all Turing machines. You can always construct a Touring machine that makes a given computer run out of memory.

So technically, no real computer or computer program is Turing complete, or able to accurately simulate any Turing machine. The whole thing is an irrelevant technicality though, as A) we have so much memory available that we might as well treat it as unlimited and B) touring completeness is a theoretical property - if you prove it for something like python type hints, that proof won’t assume any memory limitations, ie. it’ll assume the computer the thing runs on has infinite memory. The proof is valid even though no such infinite computer actually exists.