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According-to-wikipedia-the-cardonality-of-a-set-of-all-finite-subsets-of-any-countably-infinite-set-is-0-How-can-we-prove-this-




Question Number 5088 by FilupSmith last updated on 11/Apr/16
According to wikipedia,  the cardonality of a set of all finite  subsets of any countably infinite set  is ℵ_0 .    How can we prove this?
$$\mathrm{According}\:\mathrm{to}\:\mathrm{wikipedia}, \\ $$$$\mathrm{the}\:\mathrm{cardonality}\:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:{finite} \\ $$$$\mathrm{subsets}\:\mathrm{of}\:\mathrm{any}\:\mathrm{countably}\:\mathrm{infinite}\:\mathrm{set} \\ $$$$\mathrm{is}\:\aleph_{\mathrm{0}} . \\ $$$$ \\ $$$$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{prove}\:\mathrm{this}? \\ $$

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