My Math Forum Closed set

 Real Analysis Real Analysis Math Forum

 June 5th, 2018, 07:01 AM #1 Member   Joined: Apr 2017 From: India Posts: 34 Thanks: 0 Closed set The set S = {1-(1/n): n belongs to N} is a closed set. True of False. Justify your answer. Just to be more informative. A set S is called a closed set if it contains all its limit points. Please help me with the answer.
 June 5th, 2018, 07:07 AM #2 Senior Member   Joined: Aug 2012 Posts: 1,972 Thanks: 550 Have you any thoughts on the matter? Why might it be a closed set? Why might it not be a closed set? If a set is closed if it contains all its limit points, what are the limit points of your set? Does your set contain them?
 June 5th, 2018, 07:10 AM #3 Senior Member   Joined: Aug 2017 From: United Kingdom Posts: 211 Thanks: 64 Math Focus: Algebraic Number Theory, Arithmetic Geometry Hint: what's the limit of $1 - \frac{1}{n}$ as $n$ tends to infinity?
 June 6th, 2018, 03:16 AM #4 Member   Joined: Apr 2017 From: India Posts: 34 Thanks: 0 It will be 1. But 1 does not belong to the set. All the very near points to 1 belong to S, but 1 itself does not belong to that. Is this the reason why it is not a closed set? Or is it a closed set as 1 belongs to it? Last edited by skipjack; June 6th, 2018 at 09:03 AM.
 June 17th, 2018, 11:12 AM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 You say "But 1 does not belong to the set" but then ask "Or is it a closed set as 1 belongs to it?"???

 Tags closed, real analysis, set

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Lalitha183 Number Theory 2 February 25th, 2017 06:36 PM yuceelly Topology 3 March 8th, 2016 09:45 AM E7.5 Calculus 2 February 25th, 2014 04:56 AM Vasily Real Analysis 3 February 4th, 2013 12:49 PM 03sqq Real Analysis 4 November 13th, 2012 03:40 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top