My Math Forum The largest limit point of a set

 Real Analysis Real Analysis Math Forum

 December 1st, 2011, 10:08 PM #1 Member   Joined: Dec 2006 Posts: 90 Thanks: 0 The largest limit point of a set Let $S\subset\mathbb{R}$ is a bounded infinite set.denote $s*$ for the largest limit point of $S$. show that $s*=\inf\{v\in\mathbb{R}\text{; \ } v
 December 2nd, 2011, 02:35 AM #2 Senior Member   Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0 Re: The largest limit point of a set Let $v^\ast=\inf\{v\in\mathbb{R}\,:\,v\,<\,s\text{ for finitely many }s\in S\}.=$ Try to prove both that $v^\ast\,\geq\,s^\ast$ and $v^\ast\,\leq\,s^\ast.$ The first can be done easily by contradiction; for the second, just show that $s^\ast+\epsilon\in\{v\in\mathbb{R}\,:\,v\,<\,s\tex t{ for finitely many }s\in S\}$ for any $\epsilon\,>\,0.$

 Tags largest, limit, point, set

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post kaybees17 Real Analysis 2 November 8th, 2013 01:59 AM alejandrofigueroa Real Analysis 5 October 22nd, 2013 04:56 AM xdeimos99 Real Analysis 4 October 18th, 2013 07:01 PM math221 Calculus 7 February 2nd, 2013 12:02 AM xanadu Real Analysis 4 July 31st, 2009 08:36 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top