problems-2-224-S08 - MATH 224 PROBLEM SET 2 DUE: 5 FEBRUARY...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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).

Page1 / 2

problems-2-224-S08 - MATH 224 PROBLEM SET 2 DUE: 5 FEBRUARY...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online