“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
“The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.” FallNumbersMathematicsIrrationalFiniteIrrationalityIrrational Numbers 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
