The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
Georg CantorIn mathematics the art of proposing a question must be held of higher value than solving it.
Georg CantorI entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.
Georg CantorWhat 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.
Georg Cantor