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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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