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Basic topology proof

  1. Aug 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Let E be a nonempty set of real numbers which is bounded above. Let y=sup E. Then y [itex]\in[/itex] E closure. Hence y [itex]\in[/itex] E if E is closed.

    2. Relevant equations

    E closure = E' [itex]\cup[/itex] E where E' is the set of all limit points of E.

    3. The attempt at a solution

    By the definition of closure, y is either in E' or E (maybe in both). If E is closed, E' [itex]\subset[/itex] E and we know that the union of a set and its subset is the set itself. Therefore E closure = E.

    Is this a valid proof?
  2. jcsd
  3. Aug 22, 2012 #2
    Shouldn't you be proving that if y=sup(E), then y ∈ E closure?
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