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Unformatted text preview: A, B, C , and two functions f : A B , g : B C , deFne what g f is. If g f is injective, what can we say about f and g ? What if g f is surjective? 5. Prove that Z n and Z are equinumerous for all n N . 6. Show by induction that for any positive real numbers a 1 , . . . , a n , ( a 1 . . . a n ) 1 /n a 1 + + a n n . (1) 7. Show that every real number is the limit of a sequence of rational numbers. 1...
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- Fall '08