Three beliefs that lend illusory legitimacy to Cantor's diagonal argument

Mathematics – General Mathematics

Scientific paper

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v2; introduced standardised ACI compliant notation for citations; 15 pages; an HTML version is available at http://alixcomsi.c

Scientific paper

Whatever other beliefs there may remain for considering Cantor's diagonal argument as mathematically legitimate, there are three that, prima facie, lend it an illusory legitimacy; they need to be explicitly discounted appropriately. The first, Cantor's diagonal argument defines a non-countable Dedekind real number; the second, Goedel uses the argument to define a formally undecidable, but interpretively true, proposition; and the third, Turing uses the argument to define an uncomputable Dedekind real number.

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