Please explain the solution (Real Analysis)

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phillyolly
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  • Printed page with the problem 'Prove that the set of all finite subsets of N is countable' followed by a written proof using injections and disjoint unions of countable sets, ending with a Q.E.D. box.
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Discussion

What parts do you get? What parts are you having trouble with?
 
My understanding shuts down in the second paragraph, second sentence.
 
Do you understand why [tex]\textbf{N}^k[/tex] is countable?
 

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