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 Math Central Quandaries & Queries
 Question from Pretzie: What is Finite Set & Infinite Set?

Hi,

Whether a set is finite or infinite depends on the number of elements it has. First of all the empty set, the set with no elements, is finite. Suppose $S$ is a non-empty set. $S$ is a finite set if there is a positive integer $n$ such that the elements of $S$ are in a 1-to-1 correspondence with the elements of the set $\{ 1, 2, 3, \cdot, \cdot, \cdot, n\}.$ If $S$ is a set and $S$ is not finite it is defined to be infinite.

Penny

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