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Category: Set Theory

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

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

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N-0-1-2-N-0-I-know-that-if-S-k-0-1-2-S-N-0-Because-you-can-forever-pair-one-value-from-one-set-to-another-In-my-question-bellow-I-use-the-word-combine-

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Question Number 5080 by FilupSmith last updated on 10/Apr/16 $$\boldsymbol{{N}}\:=\:\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right\} \\ $$$$\mid\boldsymbol{{N}}\mid\:=\:\aleph_{\mathrm{0}} \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{know}\:\mathrm{that}: \\ $$$$\mathrm{if}\:\:\boldsymbol{{S}}\:=\:\left\{{k},\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right\} \\ $$$$\therefore\:\mid\boldsymbol{{S}}\mid\:=\:\mid\boldsymbol{{N}}\mid\:=\:\aleph_{\mathrm{0}} \\ $$$$\mathrm{Because}\:\mathrm{you}\:\mathrm{can}\:\mathrm{forever}\:\mathrm{pair}\:\mathrm{one}\:\mathrm{value} \\ $$$$\mathrm{from}\:\mathrm{one}\:\mathrm{set}\:\mathrm{to}\:\mathrm{another}. \\…

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