Hello, I have been having trouble with the following problem:
**E means epsilon**
Suppose k >= 3, x,y E R^k, |x - y| = d>0, and r>0. Prove that if 2r > d, there are infinitely many z E R^k such that |z - x| = |z - y| = r.
I'm not sure where to go with this problem...I've tried using the inequalities defined for Euc. Spaces in my text i.e.:
|z - y| <= |z - x| + |x - y|
|x - y| <= |x - z| + |z - y|
But I'm not sure if manipulating these inequalities is going to get me where I need to go. Any help with this problem would be much appreciated thank you.