$S = 1,1.1,0.9,1.01,cdots$

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$S = 1,1.1,0.9,1.01,cdots$



The following conclusions I drew from the set:



The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.



The interior of the set is empty. The set is closed, and hence compact.



What will be the limit points of the set?



Also please verify the conclusions. Thank You.










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    up vote
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    down vote

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    $S = 1,1.1,0.9,1.01,cdots$



    The following conclusions I drew from the set:



    The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.



    The interior of the set is empty. The set is closed, and hence compact.



    What will be the limit points of the set?



    Also please verify the conclusions. Thank You.










    share|cite|improve this question























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      $S = 1,1.1,0.9,1.01,cdots$



      The following conclusions I drew from the set:



      The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.



      The interior of the set is empty. The set is closed, and hence compact.



      What will be the limit points of the set?



      Also please verify the conclusions. Thank You.










      share|cite|improve this question













      $S = 1,1.1,0.9,1.01,cdots$



      The following conclusions I drew from the set:



      The set is bounded with $sup S = 1.1$ and $inf S = 0.9$, thus the bound is attained by the set.



      The interior of the set is empty. The set is closed, and hence compact.



      What will be the limit points of the set?



      Also please verify the conclusions. Thank You.







      calculus real-analysis elementary-set-theory supremum-and-infimum






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      asked Aug 30 at 4:27









      user8795

      5,36561843




      5,36561843




















          1 Answer
          1






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          up vote
          0
          down vote



          accepted










          All your conclusions are correct.



          The only limit point of the set is $1$,since you are approaching from both sides.



          All the other points are isolated points.






          share|cite|improve this answer




















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            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            0
            down vote



            accepted










            All your conclusions are correct.



            The only limit point of the set is $1$,since you are approaching from both sides.



            All the other points are isolated points.






            share|cite|improve this answer
























              up vote
              0
              down vote



              accepted










              All your conclusions are correct.



              The only limit point of the set is $1$,since you are approaching from both sides.



              All the other points are isolated points.






              share|cite|improve this answer






















                up vote
                0
                down vote



                accepted







                up vote
                0
                down vote



                accepted






                All your conclusions are correct.



                The only limit point of the set is $1$,since you are approaching from both sides.



                All the other points are isolated points.






                share|cite|improve this answer












                All your conclusions are correct.



                The only limit point of the set is $1$,since you are approaching from both sides.



                All the other points are isolated points.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Aug 30 at 4:36









                Mohammad Riazi-Kermani

                31k41853




                31k41853



























                     

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