If $(|x_n|)_n$ and $(|y_n|)_n$ are increasing, is $(|x_n+y_n|)_n$?

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Let $(x_n)_n$ and $(y_n)_n$ be two sequences of complex numbers such that




  • $(x_n)_n$ and $(y_n)_n$ are bounded.


  • $(|x_n|)_n$ and $(|y_n|)_n$ are increasing.


Is $(|x_n+y_n|)_n$ increasing? If not, I hope to find a counter-example.





real-analysis




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    up vote
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    down vote

    favorite












    Let $(x_n)_n$ and $(y_n)_n$ be two sequences of complex numbers such that




    • $(x_n)_n$ and $(y_n)_n$ are bounded.


    • $(|x_n|)_n$ and $(|y_n|)_n$ are increasing.


    Is $(|x_n+y_n|)_n$ increasing? If not, I hope to find a counter-example.





    real-analysis




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Let $(x_n)_n$ and $(y_n)_n$ be two sequences of complex numbers such that




      • $(x_n)_n$ and $(y_n)_n$ are bounded.


      • $(|x_n|)_n$ and $(|y_n|)_n$ are increasing.


      Is $(|x_n+y_n|)_n$ increasing? If not, I hope to find a counter-example.





      real-analysis




      share|cite|improve this question











      Let $(x_n)_n$ and $(y_n)_n$ be two sequences of complex numbers such that




      • $(x_n)_n$ and $(y_n)_n$ are bounded.


      • $(|x_n|)_n$ and $(|y_n|)_n$ are increasing.


      Is $(|x_n+y_n|)_n$ increasing? If not, I hope to find a counter-example.






      real-analysis





      share|cite|improve this question










      share|cite|improve this question




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      asked Jul 16 at 12:39









      Schüler

      1,3661321




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          Consider $x_n=1-1/n$ and $y_n = -(1-2/n)$.






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            up vote
            5
            down vote



            accepted










            Consider $x_n=1-1/n$ and $y_n = -(1-2/n)$.






            share|cite|improve this answer

























              up vote
              5
              down vote



              accepted










              Consider $x_n=1-1/n$ and $y_n = -(1-2/n)$.






              share|cite|improve this answer























                up vote
                5
                down vote



                accepted







                up vote
                5
                down vote



                accepted






                Consider $x_n=1-1/n$ and $y_n = -(1-2/n)$.






                share|cite|improve this answer













                Consider $x_n=1-1/n$ and $y_n = -(1-2/n)$.







                share|cite|improve this answer













                share|cite|improve this answer



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                answered Jul 16 at 12:42









                Henning Makholm

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