“The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.” MayWholeHandsRealityUsedNumbersCasesConceptsConsequenceBasesProofDistinctionNeglectQuantityEntityPropositionsAxioms Author:Georg Cantor
“The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.” MeanMatterValuesGreaterLimitsInfiniteAssumingQuantityFiniteVariables Author:Georg Cantor
“There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.” FactsDoubtInfiniteNo DoubtQuantityVariables Author:Georg Cantor
