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Unformatted text preview: MATH 224 PROBLEM SET 2 DUE: 5 FEBRUARY 2008 When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. 4.34.5. Problems from the book: 4.3.1, 4.3.4 4.4.3 4.5.2, 4.5.4 Additional problems: 1. Define f : [ 0, 1 ] R by f ( x ) = braceleftbigg sin ( 1 x ) x > 0 x = . Is f integrable on [ 0, 1 ] ? 2. Let Q denote the set of rational numbers. a. For , R , we say if  Q . Show that is an equivalence relation. b. For any R , let X = { R  } be the equivalence class of . Show r Q implies that X = X + r . c. For each distinct X , choose a representative in [ 0, 1 ) , and let Y denote the set of representatives (this requires the Axiom of Choice ...). For z R , define its reduction mod 1 to be the unique number x z [ 0, 1 ) such that z x z Z . For X [ 0, 1 ) , and y R , we define X + y to be the set of reductions mod 1 of all...
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This homework help was uploaded on 02/24/2008 for the course MATH 2240 taught by Professor Taraholm during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 TARAHOLM

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