The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.
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"Mitteilungen" (1887-8)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
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
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
As for the mathematical infinite, to the extent that it has found a justified application in science and contributed to is usefulness, it seems to me that it has hitherto appeared principally in the role of a variable quantity, which either grows beyond all bounds or diminishes to any desired minuteness, but always remains finite. I call this the improper infinite [das Uneigentlich-unendliche].
Georg Cantor
Cantor, Georg
Capa, Robert
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