Smullyan, infinity and something more

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The question, raised a couple of weeks ago, of proving that the set of all finite sets of N (N being the set of natural numbers, that is, integers and positive) is countable, remained pending. The clearest and simplest proof can be found in the excellent book by Raymond Smullyan Satan, Singer and the Infinite (which is not the first time I cite in this section nor will it be the last):

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