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infinite mathematical extension


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1 فلسفه:: توسیع نامتناهی ریاضی

Rejection of Infinite Mathematical Extensions: Given that a mathematical extension is a symbol ('sign') or a finite concatenation of symbols extended in space, there is a categorical difference between mathematical intensions and (finite) mathematical extensions, from which it follows that "the mathematical infinite" resides only in recursive rules (i.e. An infinite mathematical extension (i.e. , a completed, infinite mathematical extension) is a contradiction-in-terms Anti-Foundationalist Account of Real Numbers: Since there are no infinite mathematical extensions, irrational numbers are rules, not extensions. Rejection of Different Infinite Cardinalities: Given the non-existence of infinite mathematical extensions, Wittgenstein rejects the standard interpretation of Cantor's diagonal proof as a proof of infinite sets of greater and lesser cardinalities.

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