In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite set or a countably infinite set. Whether finite or infinite, the elements of a countable set can always be counted one at a time and, although the counting may never finish, every ...
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http://en.wikipedia.org/wiki/Countable_set
(from the article `automata theory`) The finiteness of the list of quadruples of instructions leads to the idea that all Turing machines can be listed—that is, they are at most countable ... ...According to a central discovery made in 1963 by the American mathematician Michael Morley, if a theory is categorical in any uncountable ....
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http://www.britannica.com/eb/a-z/c/149
A set that is either finite or countably infinite. A countably infinite set is one that can be put in one-to-one correspondence with the natural numbers and thus has a cardinal number ('size') of aleph-null. Examples of countable sets include the set of all people on Earth and the set of all fractio...
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http://www.daviddarling.info/encyclopedia/C/countable_set.html
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