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A set is finite if there exists some integer k such that the number of elements in k is less than k. A set is infinite if there is no such integer: that is, given any integer k, the number of elements in the set exceed k.

Infinite sets can be divided into countably infinite and uncountably infinite. A countably infinite set is one whose elements can be mapped, one-to-one, to the set of integers whereas an uncountably infinite set is one in which you cannot.

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Finite: If you count the elements in the set, you will eventually come to an end.Infinite: You'll never reach an end, no matter how long you count.

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Q: What is infinite and finite set in math?
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