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**adkinsjr** The approach I am supposed to use is to show $\displaystyle \exists p\in [0,\infty)$ such that any open ball $\displaystyle B_r(p)$ centered at $\displaystyle p$ with $\displaystyle r>0$ is not in $\displaystyle [0,\infty)$. The space is in R, so the ball is in R as well. I can express the ball as $\displaystyle B_r(p)=(p-r, p+r)$. The $\displaystyle p$ we are looking for should be $\displaystyle 0$, so the ball is $\displaystyle B_r(0)=(-r,r)$. Clearly any $\displaystyle r>0$ will give an interval with points outside of $\displaystyle [0,\infty)$. I am very bad with proofs, but I don't believe I can just say $\displaystyle (-r,r)$ is not in $\displaystyle [0,\infty)$ since $\displaystyle -r<0$ for $\displaystyle r>0$ and therefore there are points in the ball not in $\displaystyle [0,\infty)$ and be done. How can I finish this?