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which of the following metric spaces are complete?
I have doubt to this problem., $X=(0,\pi/2)$ and the metric is $d(x,y)=|\tan x-\tan y|$ is it complete metric space? I took one example $x_n=\frac{1}{2^n}$ is a cauchy sequence in $X$, $d(x_n,x_m)=|\tan\frac{1}{2^n}-\tan\frac{1}{2^m}|\rightarrow 0\notin X$, so it is not complete?