hw1 - A3. (a) Let q be an integer. Prove that if 3 divides...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Assignments for Math 140A, Fall 2011 Problem Set 1. Due Friday, September 30 Rudin, Chapter 1, pp 21-22: #1, #4, #5 Also do the following problems: A1. If A , B , and C are subsets of X , prove (carefully) that ( A \ B ) ( C \ B ) = ( A C ) \ B ) Notation: ( A \ B ) = { x A : x 6∈ B } . A2. For x and y any real numbers, prove that ± ± | x | - | y | ± ± ≤ | x - y | You may use Theorem 1.37 in the text.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A3. (a) Let q be an integer. Prove that if 3 divides q 2 , then 3 divides q . (Do not use unique factorization of integers into prime powers.) Hint: If 3 does not divide q , then q = 3 k + r , with r = 1 or r = 2. (b) Prove that there is no rational number r for which r 2 = 3. 1...
View Full Document

This note was uploaded on 09/30/2011 for the course MATH 140a taught by Professor Staff during the Fall '08 term at UCSD.

Ask a homework question - tutors are online