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Unformatted text preview: nx. 3. Prove by induction that for every n N the number 7 n4 n is divisible by 3. 4. Find and explain the aw in the proof by induction that was presented in class of the claim that all giraes are the same height (see also problem A.8.9 in the textbook). 5. Answer problems A.9.1 and A.9.2 in the textbook. 6. Prove that the set N N = { all pairs ( m,n ) where m,n N } is countable. That is, show that one can write down a list of pairs ( m 1 ,n 1 ) , ( m 2 ,n 2 ) , ( m 3 ,n 3 ) ,... covering all the elements of N N (the list may contain repetitions but any pair ( m,n ) of natural numbers must appear at least once). 2 1 Last weeks HW guidelines also still apply refresh your memory by rereading them. 2 You do not need to write a precise formula for the general term ( m k ,n k ) of this list, as long as you provide sucient detail about how to construct the list that convinces the reader that you understand what you are talking about....
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This note was uploaded on 10/16/2011 for the course MATH 34 taught by Professor Wiley during the Winter '11 term at UC Merced.
 Winter '11
 Wiley
 Differential Equations, Calculus, Equations

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