February 23rd, 2014, 07:08 PM  #1 
Newbie Joined: Feb 2014 Posts: 1 Thanks: 0  Why is this set not closed? http://i.imgur.com/Z37YCsM.png So, a set is closed if it contains all of its boundary points, and a boundary point is a point where an open ball around that point has one point inside the ball that's in the set, and one point in the ball that's not in the set. As seen in the picture, I can create infinitely many open balls around the edges of the triangle, with the balls containing at least one point in the triangle (red point) and one point outside the triangle (blue point). Since the perimeter of the triangle has all the boundary points, this triangle should be closed, but it's not. Why isn't it, if it contains all its boundary points? 
February 23rd, 2014, 09:15 PM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Why is this set not closed?
Maybe this will help. http://www.youtube.com/watch?v=FHL4udeLf9Q My signature (at the bottom of my post) has a link to the entire series of videos about the basics of higher mathematics , if you're interested. 
February 25th, 2014, 05:56 AM  #3  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Why is this set not closed? Quote:
 

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