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Open or Close, neither, or both?

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  • Michelle Wynne
    Determine whether the given sets are open, closed, neither open nor closed, or both open and closed. 1. the union of all the closed intervals [-1+1/n, 1-1/n],
    Message 1 of 5 , Sep 1, 2008
      Determine whether the given sets are open, closed, neither open nor
      closed, or both open and closed.

      1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
      2. the intersection of all the open intervals (0,(n+1)/n)

      My guess:
      1. open only
      2. open only
    • Ahlem
      Hello , me too i guess that the two sets are open If you judge people, you have no time to love them Mother Teresa ... De: Michelle Wynne
      Message 2 of 5 , Sep 1, 2008
        Hello , me too i guess that the two sets are open




















        "If you judge people, you have no time to love them"

        Mother Teresa







        --- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a écrit :
        De: Michelle Wynne <michwynne@...>
        Objet: [MATH for FUN] Open or Close, neither, or both?
        À: mathforfun@yahoogroups.com
        Date: Lundi 1 Septembre 2008, 9h11

        Determine whether the given sets are open, closed, neither open nor
        closed, or both open and closed.

        1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
        2. the intersection of all the open intervals (0,(n+1)/n)

        My guess:
        1. open only
        2. open only


        ------------------------------------

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        [Non-text portions of this message have been removed]
      • Ahlem
        [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed set is not always closed and this union tends to ]-1,1[ so it s an opened set the
        Message 3 of 5 , Sep 1, 2008
          [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed set is not always closed and this union tends to ]-1,1[ so it's an opened set
          the enumerable  intersection of an open set is an open set so the second one is open





















          "If you judge people, you have no time to love them"

          Mother Teresa







          --- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a écrit :
          De: Michelle Wynne <michwynne@...>
          Objet: [MATH for FUN] Open or Close, neither, or both?
          À: mathforfun@yahoogroups.com
          Date: Lundi 1 Septembre 2008, 9h11

          Determine whether the given sets are open, closed, neither open nor
          closed, or both open and closed.

          1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
          2. the intersection of all the open intervals (0,(n+1)/n)

          My guess:
          1. open only
          2. open only


          ------------------------------------

          Yahoo! Groups Links






          _____________________________________________________________________________
          Envoyez avec Yahoo! Mail. Une boite mail plus intelligente http://mail.yahoo.fr

          [Non-text portions of this message have been removed]
        • Renato Alencar Adelino da Costa
          See the first exercises of chapter 2 in bartle: elements of Lebesgue integration for clues. Michelle Wynne escreveu: Determine
          Message 4 of 5 , Sep 1, 2008
            See the first exercises of chapter 2 in bartle: elements of Lebesgue integration for clues.

            Michelle Wynne <michwynne@...> escreveu: Determine whether the given sets are open, closed, neither open nor
            closed, or both open and closed.

            1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
            2. the intersection of all the open intervals (0,(n+1)/n)

            My guess:
            1. open only
            2. open only






            ---------------------------------
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            [Non-text portions of this message have been removed]
          • video_ranger
            ... set is not always closed and this union tends to ]-1,1[ so it s an opened set ... second one is open I think the intersection of a *finite* number of open
            Message 5 of 5 , Sep 1, 2008
              --- In mathforfun@yahoogroups.com, Ahlem <is.dreams@...> wrote:
              >
              > [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed
              set is not always closed and this union tends to ]-1,1[ so it's an
              opened set
              > the enumerable  intersection of an open set is an open set so the
              second one is open

              I think the intersection of a *finite* number of open sets is always
              open, but this (infinite) intersection is the half open interval
              (0,1] neither open nor closed.



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              > "If you judge people, you have no time to love them"
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              > Mother Teresa
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              > --- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a
              écrit :
              > De: Michelle Wynne <michwynne@...>
              > Objet: [MATH for FUN] Open or Close, neither, or both?
              > À: mathforfun@yahoogroups.com
              > Date: Lundi 1 Septembre 2008, 9h11
              >
              > Determine whether the given sets are open, closed, neither open nor
              > closed, or both open and closed.
              >
              > 1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...
              > 2. the intersection of all the open intervals (0,(n+1)/n)
              >
              > My guess:
              > 1. open only
              > 2. open only
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              > Yahoo! Groups Links
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              ______________________________________________________________________
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              > Envoyez avec Yahoo! Mail. Une boite mail plus intelligente
              http://mail.yahoo.fr
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              > [Non-text portions of this message have been removed]
              >
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