“At the basis of the distance concept lies, for example, the concept of convergent point sequence and their defined limits, and one can, by choosing these ideas as those fundamental to point set theory, eliminate the notions of distance.” (Felix Hausdorff)
"A set is a Many that allows itself to be thought of as a One." (Georg Cantor)
"An infinite set is one that can be put into a one-to-one correspondence with a proper subset of itself." (Georg Cantor)
"Everyone agrees that, whether or not one believes that set theory refers to an existing reality, there is a beauty in its simplicity and in its scope." (Paul Cohen)
"If you can take away some of the terms of a collection, without diminishing the number of terms, then there is an infinite number of terms in the collection." (Bertrand Russell)
"Many mathematicians continue to reject the axiom of choice. The growing realization that there are questions in mathematics that cannot be decided without this principle is likely to result in the gradual disappearance of the resistance to it." (Ernst Steinitz)
"Point set topology is a disease from which the human race will soon recover." (Henri Poincaré)
"There is an old maxim that says that two empires that are too large will collapse. The analog in set theory is that two different theories that are too powerful must necessarily contradict each other." (Saharon Shelah)
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