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Unformatted text preview: Review Sheet for second test math 2030 Spring 2010 1) a)What does it mean for a set to be countably infinite. b) Prove that the Cantor set is not countably infinite. 2) Let T ( x ) = ( 3 x, if 0 ≤ x ≤ 1 2 3- 3 x, if 1 2 ≤ x < 1 . a) Sketch the graph of T and show by graphical analysis that if x < 0 or x > 1 that T n ( x ) → -∞ . b) Describe the orbit of 1 / 4 under T . Is it periodic, fixed, eventually periodic, or eventually fixed. c) Describe the orbit of 12 / 13 under T . Is it periodic, fixed, eventually periodic, or eventually fixed. d) Describe the orbit of 3 / 40 under T . Is it periodic, fixed, eventually periodic, or eventually fixed. e) Show that if x ∈ (1 / 3 , 2 / 3), then T n ( x ) → -∞ as n → ∞ . 3) What three conditions need to hold for a function d : X × X → R to be a metric. 4) What is the metric on Σ, the space of sequences of zeros and ones. 5) Compute the distance in Σ between a) s = ( 100), and t = 010)....
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This note was uploaded on 04/14/2010 for the course MATH 2030 taught by Professor Gilmer during the Spring '10 term at LSU.
- Spring '10