mockmidterm - k is separable for all k IN. 5. Determine all...

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Mock midterm test. 1. Is the number q 2 + 2 rational? 3. Are the following subsets of C (identified with IR 2 ) (a) open (b) closed (c) perfect (d) connected (e) bounded, with respect to the standard metric | · | on C ? 1. { z ZZ : | z 2 - 1 | < 1 } 2. { m + i n : m, n ZZ } 3. { 1 /m + i /n : m, n IN } 4. A metric space is called separable if it contains a countable dense set. Show that IR
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Unformatted text preview: k is separable for all k IN. 5. Determine all the limit points, lim inf and lim sup of the sequence (-1) n 1 + sin( n/ 2) + sin(3 n/ 2) ! n IN . 6. Determine for which z C the power series X n =0 z n 1 + n converges....
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