2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67173Whatever 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.htmGeneral Mathematics03B10text