Question: Prove that if S is a countably infinite set then all the finite subsets of S are also countably infinite.
Where would I start?
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2Do you mean that the set of all finite subsets of $S$ is countably infinite -- or (as Nilknarf assumed) that each infinite subset of $S$ is (by itself) countably infinite? – hmakholm left over Monica Oct 19 '17 at 23:43
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https://math.stackexchange.com/questions/361320/neatest-proof-that-set-of-finite-subsets-is-countable – User8976 Oct 19 '17 at 23:57
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No, all the finite subsets are not infinite because each of them is finite. None of them are infinite for all of themare finite. – William Elliot Oct 20 '17 at 01:57