What I declare and believe to have demonstrated in this work as well as in earlier papers is that following the finite there is a transfinite (transfinitum)--which might also be called supra-finite (suprafinitum), that is, there is an unlimited ascending ladder of modes, which in its nature is not finite but infinite, but which can be determined as can the finite by determinate, well-defined and distinguishable numbers.
Georg CantorRelated topics
ascending believe determinate early following infinite ladder might nature numbers well work papers transfiniteRelated quotes
A child free from the guilt of ownership and the burden of economic competition will grow up with the will to do what needs doing and the capacity for joy in doing it. It is useless work that darkens the heart. The delight of the nursing mother, of the scholar, of the successful hunter, of the good cook, of the skilful maker, of anyone doing needed work and doing it well, - this durable joy is perhaps the deepest source of human affection and of sociality as a whole.
Ursula K. Le Guin
Entities other than Brahman can be objects of such cognitions of the nature of joy only to a finite extent and for limited duration. But Brahman is such that cognizing of him is an infinite and abiding joy. It is for this reason that the shruti [scripture] says, `Brahman is bliss' (Taittitriya Upanishad II.6.) Since the form of cognition as joy is determined by its object, Brahman itself is joy.
Ramanuja
I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.
Georg Cantor
That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.
Georg Cantor
The multitude will hardly believe the excessive force of education, and in the difference of modesty between men and women, ascribe that to nature, which is altogether owing to early instruction: Miss is scarce three years old, but she's spoke to every day to hide her leg, and rebuked in good earnest if she shows it; whilst little Master at the same age is bid to take up his coats, and piss like a man.
Bernard Mandeville
