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

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

2003-04-21

arxiv.org/abs/math/0304310v2

Mathematics

General Mathematics

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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