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A finite set is a set with a finite number of elements. An infinite set has an infinite number of elements. Intuitively, if you count the elements in a finite set, you will eventually finish counting; with an infinite set, you'll never finish counting. One characteristic of infinite sets is that they can be placed in one-to-one correspondence with proper subsets of the set. For example, if A = {1, 2, 3, 4, ...} (the counting numbers), and B = {2, 3, 4, 5, ...} (the counting numbers, starting at 2), then B is a proper subset of A, and they can be placed in one-to-one correspondence like this: 1 <---> 2; 2 <---> 3; 3 <---> 4, etc. This means that, in a certain sense, the set and its proper subset have "the same number of elements". Such a one-to-one correspondence (between a set and one of its proper subsets) is not possible with finite sets.

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โˆ™ 2012-06-18 12:20:00
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Q: What are finite and infinite sets?
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