Georg Cantor Quotes
A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held.
In Mathematics the art of proposing a question must be held of higher value than solving it.
Don't always blindly follow guidance and step-by-step instructions; you might run into something interesting.
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.
Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
![Georg Cantor Quotes: "The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers."](https://www.quoteslyfe.com/images/collection3/quotations603/The-transfinite-numbers-are-in-a-sense-603499.jpg)
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.
Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!
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In mathematics the art of proposing a question must be held of higher value than solving it.
I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.