Philosophical Enquiries

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How to Pair the Real Numbers with the Integers: a Game of Kitchen Mathematics.pdf
(2023) Cameron, Evan Wm.;
Can 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.