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Georg Cantor Quotes

A set is a Many that allows itself to be thought of as a One Picture Quote #1

The essence of mathematics lies entirely in its freedom Picture Quote #1

The essence of mathematics lies in its freedom Picture Quote #1

Great innovation only happens when people aren’t afraid to do things differently Picture Quote #1

My beautiful proof lies all in ruins Picture Quote #1

In mathematics, the art of asking questions is more valuable than solving problems Picture Quote #1

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To ask the right question is harder than to answer it Picture Quote #1

In mathematics the art of proposing a question must be held of higher value than solving it Picture Quote #1

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 Picture Quote #1

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds Picture Quote #1

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 Picture Quote #1

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 Picture Quote #1

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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 Picture Quote #1

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 to speak, to the first infallible cause of all created things Picture Quote #1

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 Picture Quote #1

Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number Picture Quote #1

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A set is a Many that allows itself to be thought of as a One (Georg Cantor Quotes) The essence of mathematics lies entirely in its freedom (Georg Cantor Quotes) The essence of mathematics lies in its freedom (Georg Cantor Quotes) Great innovation only happens when people aren’t afraid to do things differently (Georg Cantor Quotes) My beautiful proof lies all in ruins (Georg Cantor Quotes) In mathematics, the art of asking questions is more valuable than solving problems (Georg Cantor Quotes) To ask the right question is harder than to answer it (Georg Cantor Quotes) In mathematics the art of proposing a question must be held of higher value than solving it (Georg Cantor Quotes) 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 (Georg Cantor Quotes) The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds (Georg Cantor Quotes) 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 (Georg Cantor Quotes) 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 Quotes) 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 (Georg Cantor Quotes) 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 to speak, to the first infallible cause of all created things (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 (Georg Cantor Quotes) Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number (Georg Cantor Quotes)