psAnalysis3Qu - Fall 2007 ARE211 Problem Set #03 Third...

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: Fall 2007 ARE211 Problem Set #03 Third Analysis Problem Set Due date: Sep 25 Problem 1 For the following problem, consider an arbitrary universe X and an arbitrary metric d defined on X × X . State whether the following statements are true or false. If they are true, give a proof. If they are wrong, give a counter-example a) If a sequence x n converges then every subsequence of x n must also converge. b) If every subsequence of the sequence x n converges, then x n must also converge. c) If every subsequence of the sequence x n converges, then they all converge to the same point. d) If one subsequence of the sequence x n converges, then x n must also converge. Problem 2 For the following problem, consider an arbitrary universe X and an arbitrary metric d defined on X × X . You are given a sequence x n . Consider the set S = { x n } ∞ n =1 (The set consists of all elements in the sequence). Prove that if b is an accumulation point of the set S, then some subsequence of x n converges to b.converges to b....
View Full Document

This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at University of California, Berkeley.

Page1 / 4

psAnalysis3Qu - Fall 2007 ARE211 Problem Set #03 Third...

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