 Quote by Hurkyl
You guys aren't being fair. IIRC, his math is quite sound. His only problem is an equivocation fallacy -- he is invoking alternative treatments of the notion of "real number", when everybody else is using the term in its standard meaning.
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Actually, I rather agree that most of what he says appears sound, and much of the remainder could be salvaged with some rigor. Certainly I have no problem with people exploring alternate systems.
But saying that Turing proved that not all reals have decimal expansions... that's just crazy talk.