You can iterate over all finite algorithms, but you can’t reliably tell which of these algorithms will output an infinite string, or a finite string, or get stuck at some point in an infinite loop (unless you have a halting oracle).
You couldn’t even iterate over “the first character outputted by finite algorithm number n”, let alone the nth one.
You can iterate over all finite algorithms, but you can’t reliably tell which of these algorithms will output an infinite string, or a finite string, or get stuck at some point in an infinite loop (unless you have a halting oracle).
You couldn’t even iterate over “the first character outputted by finite algorithm number n”, let alone the nth one.
Essentially, I agree with you. The algorithm I defined with this diagonalization method is in fact NOT finite.
What is just fine.