MATH 323 Midterm: Math 323 exam1-old
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31 Jan 2019
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Partial credit is possible, but you must show all work. I hereby testify that this is individual work. Signed: (a) use induction to show that n7 n is always divisible by 7 for n n. (b) show that n9 n is not necessarily divisible by 9 for n n. 2: let a, b r be two nonempty subsets. A + b = {x + y : x a, y b}. Show that a + b is countable if both a and b are: (a) use any method to prove that, a, b r, n. Xk=0 (a + bk) = (n + 1) (2a + bn) 2: consider the relation de ned on z by: n m if n2 = m2. Show that is a well-de ned 1-1 correspondence. 4: let (a, b) = {x r : a < x < b}.
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