Three beliefs that lend illusory legitimacy to Cantor's diagonal argument
Abstract
Description
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.
v2; introduced standardised ACI compliant notation for citations; 15 pages; an HTML version is available at http://alixcomsi.com/Three_beliefs.htm
v2; introduced standardised ACI compliant notation for citations; 15 pages; an HTML version is available at http://alixcomsi.com/Three_beliefs.htm