I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of… — Georg Cantor Copy Share
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 Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not - I do not say… — Georg Cantor Copy Share
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? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so… — Georg Cantor Copy Share
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 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, however, this "axiom" is used innumerably often without any… — Georg Cantor Copy Share
In mathematics the art of proposing a question must be held of higher value than solving it. — Georg Cantor Copy Share Image
