“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
“Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.” IdeasRealityDevelopmentConceptsAccountsMathematicsObligationTransient Author:Georg Cantor
“Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.” MeanDevelopmentConceptsMathematicsDefinitionsMathConsistentPreciseLinked Author:Georg Cantor
