How to Pair the Real Numbers with the Integers: a Game of Kitchen Mathematics.pdf

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dc.contributor.advisor
dc.contributor.authorCameron, Evan Wm.
dc.date.accessioned2021-02-09T15:38:56Z
dc.date.available2021-02-09T15:38:56Z
dc.date.issued2023
dc.description.abstractCan one pair the real numbers with the integers? I believe so, believing as well that the proof follows so simply from the work of Abraham Robinson a half-century ago that neither he nor readers thereafter, minds on other matters, noticed. Had they done so, they would have realised that the pairing obliterates the conclusion and methods of Georg Cantor's 'proofs' to the contrary and therewith his insistence that sets are required for comprehending mathematics, for were there 'no more real numbers than integers', we should have no reason to suppose that there are uncountably many things of any kind within our world, numbers included, and hence no need for them. Within this essay, I prove the pairing, unpack the flaws in Cantor's 3rd 'proof' and sketch the 'religious' passion that drive him to ignore them.en_US
dc.identifier.urihttp://hdl.handle.net/10315/38097
dc.language.isoenen_US
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Canada
dc.rights.urihttp://creativecommons.org/licenses/by-nc-d/2.5/ca/
dc.subjectArchimedes of Syracuseen_US
dc.subjectAutobiographyen_US
dc.subjectCantor, Georgen_US
dc.subjectCohen, Paul J.en_US
dc.subjectDauben, Joseph Warrenen_US
dc.subjectde Bois-Reymond, Paulen_US
dc.subjectDedekind, Richarden_US
dc.subjectGalileo Galileien_US
dc.subjectGödel, Kurten_US
dc.subjectGoodman, Nelsonen_US
dc.subjectHilbert, Daviden_US
dc.subjectJames, Williamen_US
dc.subjectPeirce, Charles Sandersen_US
dc.subjectPoincaré, Henrien_US
dc.subjectQuine, Willard Van Ormanen_US
dc.subjectRobinson, Abrahamen_US
dc.subjectTuring, Alanen_US
dc.subjectVivanti, Giulioen_US
dc.subjectWittgenstein, Ludwigen_US
dc.subjectCantor-Dedekind Axiomen_US
dc.subjectCompletenessen_US
dc.subjectDecimalsen_US
dc.subjectGamesen_US
dc.subjectGoden_US
dc.subjectIndirect Proofsen_US
dc.subjectSetsen_US
dc.subjectInfinite Setsen_US
dc.subjectInfinitesimalsen_US
dc.subjectInfinityen_US
dc.subjectIntegersen_US
dc.subjectLogicen_US
dc.subjectMathematicsen_US
dc.subjectMathematics, History ofen_US
dc.subjectNegationen_US
dc.subjectNonstandard Analysisen_US
dc.subjectPhilosophyen_US
dc.subjectPhilosophy, History ofen_US
dc.subjectRational Numbersen_US
dc.subjectReal Numbersen_US
dc.subjectReligionen_US
dc.subjectReligion, History ofen_US
dc.subjectScholasticismen_US
dc.subjectSetsen_US
dc.subjectSet Theoryen_US
dc.subjectCameron, Evan
dc.subjectAutobiography
dc.subjectCantor's Diagonal Proof
dc.titleHow to Pair the Real Numbers with the Integers: a Game of Kitchen Mathematics.pdfen_US
dc.typeArticleen_US

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