“The transfinite numbers themselves are in a certain sense new irrationals, and in fact I think the best way to define the finite irrational numbers is entirely similar; I might even say in principle it is the same as my method for introducing transfinite numbers. One can absolutely assert: the transfinite numbers stand or fall with the finite irrational numbers; they are alike in their most intrinsic nature; for the former like these latter are definite, delineated forms or modifications of the actual infinite.”