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February 24th, 2016, 08:39 PM   #11
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Originally Posted by Polaris84 View Post
But I thought that all finite sets are countable? with 3 elements and 6 subsets, the pigeon hole principal applies, and the elements must repeat.
I'm suggesting that you walk through the proof step by step for a 3 element set with an 8 element power set. Write down the domain and range, pick some functions f, define the set X, show that X can't be hit by anything.

The pigeonhole principle doesn't apply at all here, you're mapping the smaller set to the larger set.
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