I am reading kreyszig functional analysis book where I got this problem:
Let $X$ be the set of all positive integers and $d(m,n) = \mid \frac{1}{m} - \frac{1}{n} \mid$. I have to show that $(X,d)$ is not complete metric space.
I took sequence $(x_n) = (n)$ which I showed that cauchy in $X$. But, I am not sure whether I am correct or not. I am also struggling with showing that this sequence is not convergent in $X$.
Thanks for helping me