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March 15th, 2012, 06:32 AM   #1
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Infinite set contains an infinite number of subsets

How would I go about proving that an infinite set X contains an infinite number of subsets?

I thought about observing one-element subsets of set X and showing that the number of these subsets is equal to the number of elements in the set X, but I'm not sure how to properly put it on paper.

Thanks for your help.
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March 15th, 2012, 11:28 AM   #2
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Re: Infinite set contains an infinite number of subsets

Here is a simple proof: Let T be the set of all subsets of S (which is an infinite set) having exactly one element. Clearly, T is an infinite set because S has an infinite number of distinct elements.
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