“Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.” NumbersConsistentDefiniteCardinalsMultiplicity Author:Georg Cantor
“The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.” FactsMightFormCertainFallNumbersOpinionDiscoveryInfiniteMethodFormerLatterIntroducingIrrationalDefiniteFiniteDefiningEpiphanyIrrationalityModificationFinite NumberIrrational Numbers Author:Georg Cantor
“What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.” BelieveWellsNumbersDiscoveryInfiniteFollowingDeterminedDefinedDefiniteFiniteEpiphanyAscendingFinite Number Author:Georg Cantor
