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 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 ladder 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
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 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 Infinite alone exists and is Real; the finite is passing and false.
The Original Whim in the Beyond caused the apparent descent of the Infinite into the realm of the seeming finite. This is the Divine Mystery and Divine Game in which Infinite Consciousness for ever plays on all levels of finite consciousness.Meher Baba
The movement of doubt consisted precisely in this: that at one moment he was supposed to be in the right, the next moment in the wrong, to a degree in the right, to a degree in the wrong, and this was supposed to mark his relationship with God; but such a relationship with God is not relationship, and this was the sustenance of doubt. In his relationship with another person, it certainly was possible that he could be partly in the wrong, partly in the right, to a degree in the wrong, to a degree in the right, because he himself and every human being is finite, and their relationship is a finite relationship that consists in a more or less. Therefore as long as doubt would make the infinite relationship finite, and as long as wisdom would full up the infinite relationship with the finite-just so long he would remain in doubt. Thus every time doubt wants to trouble him about the particular, tell him that he is suffering too much or is being tested beyond his powers, he forget the finite in the infinite, that he is always in the wrong. Every time the cares of doubt want to make him sad, he lifts himself above the finite into the infinite, because this thought, that he is always in the wrong, is the wings upon which he soars over the finite. This is the longing with which he seeks God; this is the love which he finds God.
Soren Aabye Kierkegaard
Cantor, Georg
Capa, Robert
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