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- IIT JAM
- Mathematics (MA)
Please justify your answer and show me the solution of your proof
please justify your answer and show me the solution of your proof
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Deepak singh 1![best-answer]()
See here , irrational number (e) is the limit of a sequence of rationals. So , Q is not closed (for a set to be closed it should contain all of its limit points). Similarly there exist a sequence of irrational that converges to rational which does not contained in Qc , So Qc is also not closed ..
and [a,infinity) is closed because take any €-neigbourhood around any element of x belongs to [a,infinity ) , then this neighbourhood intersection with [a,infinity ) (excluding element) will contain infinite terms of [a,infinity )