Openness and closedness in R Decide the closedness and openness of {x:0<|x|<1 and (1/x)∉N}. I know the answer that the set is open but not closed. But I am not getting why?

Your set $A$ is open because it is equal to union of intervals $$ ( \frac{1}{n} ; \frac{1}{n + 1} )$$
and $A$ is not closed because $$ 0 \in  \mathbb{R} - A $$ but every interval $$ ( -\varepsilon ; \varepsilon)$$ have nonempty intersection with $A$
