Thought and beauty, like a hurricane or waves, should not know conventional, delimited forms.

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 dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite 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.
georg cantorAristotle says the infinite is imperfect, unfinished, and therefore unthinkable; it is formless and confused. Only as objects are delimited and distinct do they have a nature.