Hi , i have this problem , i need help with this exercise

If b $\displaystyle \notin$ B[a,r] , prove that exist s>0 such that B[a,r] $\displaystyle \cap$ B[b,s] = $\displaystyle \emptyset$

Thanks

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- Aug 23rd 2012, 10:56 AMresident911metric space
Hi , i have this problem , i need help with this exercise

If b $\displaystyle \notin$ B[a,r] , prove that exist s>0 such that B[a,r] $\displaystyle \cap$ B[b,s] = $\displaystyle \emptyset$

Thanks - Aug 23rd 2012, 11:21 AMPlatoRe: metric space
Please, please get in the habit of posting the meaning of notations that you use.

If $\displaystyle B[a,r]=\{x:d(a,x)<r\}$ the ordinary*ball*then the statement is false.

If $\displaystyle B[a,r]=\{x:d(a,x)\le r\}$ the ordinary*closed ball*then the statement is true.

Which is it? Or is it something altogether different?