Consider the set X={1,2,3,....} regarded as subspace of the set of real mumber R with usul matric .Then check the completeness, compactness and bounded(if any) of X is.....?
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The set R of all real numbers is not compact as there is a cover of open intervals that does not have a finite subcover. For example, intervals (n−1, n+1)
where n takes all integer values in Z, cover R but there is no finite subcover...
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