The document's initial example of diagonalization doesn't explain it properly. It shows how you can find a binary string that's not in the list; fine. But it's conveniently a list of 5 strings of length 5. It doesn't show how you'd find a new string of length 5 that's not in a list of 6 such strings, or 31 such strings.
I suspect the "conveniently" may drop out of some conversion of a real problem to an abstraction, but that's not explained.
I suspect the "conveniently" may drop out of some conversion of a real problem to an abstraction, but that's not explained.