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 June 1st, 2012, 03:17 PM #1 Newbie   Joined: May 2012 Posts: 14 Thanks: 0 Can you find a 4 ball contained in a 3 ball, with not equal? In a metric space, an you find an open ball $A$ with radius 4, contained in an open ball $B$ with radius 3, but $A \neq B$? Why?
 June 2nd, 2012, 01:10 PM #2 Global Moderator   Joined: May 2007 Posts: 6,704 Thanks: 670 Re: Can you find a 4 ball contained in a 3 ball, with not eq Your question is confusing. How can you have a ball of radius 4 inside a ball of radius 3?
 June 6th, 2012, 08:23 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Can you find a 4 ball contained in a 3 ball, with not eq If A is an open ball with radius 4, then, given any $\epsilon> 0$, there exist points, p and q, in A such that $d(p,q)> 4- \epsilon$. If $\epsilon< 1$, there is no ball of radius 3 containing both p and q.
 June 7th, 2012, 11:13 PM #4 Senior Member   Joined: Feb 2012 Posts: 144 Thanks: 16 Re: Can you find a 4 ball contained in a 3 ball, with not eq let S={0,2,4} and let us use the usual distance. Then S is a metric space and B(2,3)=S B(0,4)={0,2} B(a,b) is the open ball with center a and radius b.

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