MAA 3200 Midterm: MAA 3200 FIU Exam 3
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Show all your work and explain your reasoning. Don"t use your own paper, a calculator or book. You may ask for extra paper or for clari cations. Each problem is 20 points: short answer: Give an example of a number system with additive inverses that is not a eld. Given that s1 = 1 and s2 = 1 and sn+1 = sn + sn 1 (for n 2), nd s8. Give an example of a sequence that is not bounded, with lim sn/n = 0: answer true or false; do not justify. X, y n , sx( (y)) = (sx(y)). s2 : n n is onto. The set of all polynomial functions with rational coe cients is countable. 3,4) choose two to prove: prove that multiplication is commutative in z. Use the de nitions - you may assume anything you need about n : addition in n is associative.
