This is the problem stated verbatim. xo is supped to be x with a subscript o.
Suppose that A is a set and there exists xo ε A for which lx-xol ≤ r. Is it necessarily true true that for all x,y εA, we will have lx-yl ≤2r?
Well, this problem is just supposed to test our ability to formulate proofs, so I can't think of many helpful equations.
I do know lxl < r is the same thing as -r<x<r
The Attempt at a Solution
I can't even think of how to start proving this. In desperation, I tried to think of a counterexample to prove this untrue, but none came to mind. It's also weird that r is such an arbitrary value or variable or something. Nothing is stated in the problem on what it's supposed to represent. I think it means any picked real number but I'm not sure.