Dear Colleagues, Could you please help me in solving the following problem: show that the set of all real number constitutes an incomplete metric space if we choose $\displaystyle d(x,y)=|arc tan(x) - arc tan(y)|$ Best Regards
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Originally Posted by raed Dear Colleagues, Could you please help me in solving the following problem: show that the set of all real number constitutes an incomplete metric space if we choose $\displaystyle d(x,y)=|arc tan(x) - arc tan(y)|$ Best Regards What can you say about the sequence $\displaystyle (x_n)$, where $\displaystyle x_n = n$ ?
Thank you very much for your reply. But is this Cauchy. Regards, Raed.
Originally Posted by raed Thank you very much for your reply. But is this Cauchy. That is what you have to decide, using the given metric.
Originally Posted by raed But is this Cauchy. Here is a large hint: $\displaystyle \displaystyle\lim _{n \to \infty } \arctan (n) = \frac{\pi }{2}$.
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