MATH1013 Midterm: MATH 1013 UNB Exam 1013 04
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Read this first: this is a closed-book examination. No books, notes, phones, communication devices of any sort, or other aids are permitted. Phones are to be turned o and out of sight: please read each question carefully. Show all work clearly in the space provided: if you do scratch work before a proof, please label the scratch work clearly, if your proof uses a theorem proved in class, tell me which theorem. Final exam: suppose we have nonempty subsets a, b r that are bounded above. A + b = {a + b | a a, b b}. (a) [4 points] prove that a + b is bounded above. (b) [10 points] prove that sup(a + b) sup(a) + sup(b). In other words, (an) a and (bn) b. Use the de nition given in part (a) to prove that (an + bn) a + b. For each n n, de ne fn(x) = g(x) n.
