# Math Help - Incomplete Metric Space

1. ## Incomplete Metric Space

Dear Colleagues,

show that the set of all real number constitutes an incomplete metric space if we choose
$d(x,y)=|arc tan(x) - arc tan(y)|$

Best Regards

2. Originally Posted by raed
Dear Colleagues,

show that the set of all real number constitutes an incomplete metric space if we choose
$d(x,y)=|arc tan(x) - arc tan(y)|$

Best Regards
What can you say about the sequence $(x_n)$, where $x_n = n$ ?

3. Thank you very much for your reply. But is this Cauchy.

Regards,

Raed.

4. Originally Posted by raed
Here is a large hint: $\displaystyle\lim _{n \to \infty } \arctan (n) = \frac{\pi }{2}$.