In the metric space [tex](\mathbb R, d)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

1) [tex]d(x,y) = |{tan}^{ - 1}(x) - {tan}^{ - 1}(y)|[/tex] ,where x,y are real numbers .

2) [tex]d(x,y) = |{tan}^{ - 1}(x) - {tan}^{ - 1}(y)|[/tex], where x,y are real numbers .

Show that [tex](\mathbb R, d)[/tex] w.r.t (1) and (2) are incomplete metric space . Also, what is the completion space of both w.r.t. (1) and (2).

I appreciate any help.

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# Incomplete and completion

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