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Arran_Stirton comments on No one knows what Peano arithmetic doesn't know - Less Wrong
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Ah thanks, it seems I misread the whole "is there an integer N such that T takes N steps" as "is there an integer N such that T takes some number of steps then halts", sorry about that - brain malfunction I guess. Though now that I see what you mean rather than what I thought you meant, good post! Not old news to me, but them I'm relatively new to computability theory.