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Emile comments on What are you working on? December 2012 - Less Wrong
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Comments (42)
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.