Quotations, Proverbs & Sayings

Research Database of Quotes

It is sometimes difficult to be inspired when trying to write a persuasive essay, book report or thoughtful research paper. Often of times, it is hard to find words that best describe your ideas. Paper-Research now provides a database of over 150,000 quotations and proverbs from the famous inventors, philosophers, sportsmen, artists, celebrities, business people, and authors that are aimed to enrich and strengthen your essay, term paper, book report, thesis or research paper.

Try our free search of constantly updated quotations and proverbs database.

Browse Authors

(Click a letter to view the authors)
A B C D E F
G
H I J K L M N O P Q R S T U V W X Y Z

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.»
«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.»
«The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.»
«A set is a Many that allows itself to be thought of as a One.»
Author: Georg Cantor | About: Infinity | Keywords: A-one
«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.»
«In mathematics the art of proposing a question must be held of higher value than solving it.»
Author: Georg Cantor
«The essence of mathematics lies in its freedom.»
Author: Georg Cantor
«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.»
Author: Georg Cantor
«Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.»
Author: Georg Cantor
«In mathematics the art of asking questions is more valuable than solving problems.»
Author: Georg Cantor