There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated. — Georg Cantor Copy Share Image
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,… — Georg Cantor Copy Share Image
In mathematics, the art of asking questions is more valuable than solving problems. — Georg Cantor Copy Share Image
I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions… — Georg Cantor Copy Share Image
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that… — Georg Cantor Copy Share Image
The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than… — Georg Cantor Copy Share Image
My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this?… — Georg Cantor Copy Share Image
I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have… — Georg Cantor Copy Share Image
What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one… — Georg Cantor Copy Share Image
A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is… — Georg Cantor Copy Share Image
The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in… — Georg Cantor Copy Share Image
In mathematics the art of proposing a question must be held of higher value than solving it. — Georg Cantor Copy Share Image
![“The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately…” quote by Georg Cantor](https://sms4smile.com/quotes/img-quotes/1c9/georg-cantor-20252_axioms_the-old-and-oft-repeated-proposition-tot_1288544.jpg)
