A Quote by Georg Cantor
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.
Related Quotes
The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
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 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.
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.
Wealth, in terms of dollars and so forth, could be counted up, because dollars were finite. It doesn't make any difference how many dollars you have-at a certain point you only have dollars. You start with finite, you end with finite.
Wealth, in terms of dollars and so forth, could be counted up, because dollars were finite. It doesn’t make any difference how many dollars you have - at a certain point you only have dollars. You start with finite, you end with finite.
All is finite in the present; and even that finite is infinite in it velocity of flight towards death. But in God there is nothing finite...Upon a night of earthquake he builds a thousand years of pleasant habitations for man. Upon the sorrow of an infant he raises oftentimes from human intellects glorious vintages that could not else have been.
Man always worships something; always he sees the Infinite shadowed forth in something finite; and indeed can and must so see it in any finite thing, once tempt him well to fix his eyes thereon.
I dare not think that any supercelestial heaven, or whatsoever else ... was increate and eternal. And as for the place of God before the world created, the finite wisdom of mortal men hath no perception of it; neither can it limit the seat of infinite power, no more than infinite power itself can be limited; for his place is in himself, whom no magnitude else can contain.
The 'lowly' finite is MUCH more beautiful than any 'infinite'
What I've been thinking about recently is the idea of finite and fragility. Either we're acknowledging that our lives here are finite, this moment is finite, and that this whole world is fragile, or we're not, but it is really happening and that is really true.
From now on I will consider a language to be a set (finite or infinite) of sentences, each finite in length and constructed out ofa finite set of elements. All natural languages in their spoken or written form are languages in this sense.
The cause being finite, the effect must be finite. If the cause is eternal the effect can be eternal, but all these causes, doing good work, and all other things, are only finite causes, and as such cannot produce infinite result.
Nothing can be divided into more parts than it can possibly be constituted of. But matter (i.e. finite) cannot be constituted of infinite parts.
When I speak of the aspiration towards the beautiful, of the ideal as the ultimate aim of art, which grows from a yearning for that ideal, I am not for a moment suggesting that art should shun the 'dirt' of the world. On the contrary! the artistic image is always a metonym, where one thing is substituted for another, the smaller for the greater. To tell of what is living, the artist uses something dead; to speak of the infinite, he shows the finite. Substitution... the infinite cannot be made into matter, but it is possible to create an illusion of the infinite: the image.
There are at least two kinds of games. One could be called finite, the other, infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.
In any finite region of space, matter can only arrange itself in a finite number of configurations, just as a deck of cards can be arranged in only finitely many different orders. If you shuffle the deck infinitely many times, the card orderings must necessarily repeat.
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