A Quote by 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 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.
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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 disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite 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.
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.
The individual soul touches upon the world soul like a well reaches for the water table. That which sustains the universe beyond thought and language, and that which is at the core of us and struggles for expression, is the same thing. The finite within the infinite, the infinite within the 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.
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.
Far be it from us to doubt that all number is known to Him 'Whose understanding is infinite' (Ps. 147:5). The infinity of number, though there be no numbering of infinite numbers, is yet not incomprehensible by Him Whose understanding is infinite. And thus, if everything which is comprehended is defined or made finite by the comprehension of him who knows it, then all infinity is in some ineffable way made finite to God, for it is comprehensible by His knowledge.
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.
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.
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.
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.
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.
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.
All the analysis of infinite reality which the finite human mind can conduct rests on the tacit assumption that only a finite portion of this reality constitutes the object of scientific investigation, and that only it is 'important' in the sense of being 'worthy of being known.
All the analysis of infinite reality which the finite human mind can conduct rests on the tacit assumption that only a finite portion of this reality constitutes the object of scientific investigation, and that only it is 'important' in the sense of being 'worthy of being known.'
If you reject the infinite, you are stuck with the finite, and the finite is parochial... the best explanation of anything eventually involves universality, and therefore infinity. The reach of explanations cannot be limited by fiat.
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