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Vijay posted an Question
November 13, 2020 • 11:44 am 30 points
  • IIT JAM
  • Mathematics (MA)

What is the isolated point of a set of rational numbers please 🙏 justify your answer

what is the isolated point of a set of rational numbers please 🙏 justify your answer

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    Piyush pachauri best-answer

    a point x is called an isolated point of a subset S if x is an element of S but there exists a neighbourhood of x which does not contain any other points of S. Q is dense in R so No isolated point.

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    Deepak singh 1 Best Answer

    Definition - a point x is called an isolated point of a subset S , if x is an element of S but there exists a neighbourhood of x which does not contain any other points of S. Now here S= Q if you take any neighborhood of an element x belongs to Q then there will be definitely always an another point that belongs to Q . (due to denseness of rationale ) So isolated points of Q are empty (phi) .

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