MATH 320 Midterm: MATH 320 2014 Winter Test 1
Document Summary
Be sure that this examination has 11 pages including this cover. De ne (a) supremum (b) limit point of a set (c) lim x p f (x) Give an example of each of the following, together with a brief explanation of your example. If an example does not exist, explain why not. (a) a sequence (cid:0)an(cid:1)n in of real numbers, converging to 0, for which the partial sums sn = n. P k=1 ak are bounded, but ak diverges. P k=1 (b) two subsets, a and b, of a metric space for which a b 6= a b. (c) a function f : ir ir such that. |f (x) f (y)| < = |x y| < and yet f is not continuous. Prove that there is one and only one real number such that a b for all a a and b b.
