A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is said to be countable. While the meaning of the term "finite" is fairly clear in common usage, precise definitions of finite and infinite are needed in technical mathematics and especially in set theory.

See also

Countable Set, Countably Infinite, Infinite, Set Theory, Uncountably Infinite

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Weisstein, Eric W. "Finite." From MathWorld--A Wolfram Web Resource.

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