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Members of a herd of animals, for example, could be matched with stones in a sack without members of either set actually being counted. The notion extends into the infinite.

Russell’s reduction of mathematics to logic

For example, the set of integers from 1 to is finite, whereas the set of all integers is infinite. A set is commonly represented as a list of all its members enclosed in braces. Because an infinite set cannot be listed, it is usually represented by a formula that generates its elements when applied to the elements of the set of counting numbers.

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Kurt Gödel Research Center for Mathematical Logic (KGRC), Vienna

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