> I don't think you've shown that Shannon's theorem isn't a problem here so much as the argument presented did not successfully convey that it's a problem. Yes

> I don't think you've shown that Shannon's theorem isn't a problem here so much as the argument presented did not successfully convey that it's a problem. Yes, I was referring to the specific example he made, I wasn't generalizing my conclusion to all possible cases. At the moment of writing my comment I wasn't sure if there was an example that would have worked or not, but the comment about Collatz numbers is a good example. Edit: actually it could be a good example, because wheter that number can be represented in a finite way or not depends on whether Collatz's conjecture is true or false.