Can a bounded number sequence be strictly ascending?Bounded Sequence ProofEvery bounded monotone sequence convergesCauchy sequences are bounded?!Why is sequence $(1+frac1n)^n+1$ descending?Show that for a sequence $p_n$ of real numbers, $limsup p_n < +∞$ iff $p_n$ is bounded above.If $a_n$ and $b_n$ are equivalent sequences and $a_n$ is bounded then so is $b_n$.Show that $s_n$ is bounded if $s_n = b_1r + b_2r^2 + … + b_nr^n$ and $0 < r < 1$.Implicit Fact about Bounded Monotone Sequence convergesBolzano-Weierstrass boundedProve that if a sequence is eventually bounded then it is bounded

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Can a bounded number sequence be strictly ascending?


Bounded Sequence ProofEvery bounded monotone sequence convergesCauchy sequences are bounded?!Why is sequence $(1+frac1n)^n+1$ descending?Show that for a sequence $p_n$ of real numbers, $limsup p_n < +∞$ iff $p_n$ is bounded above.If $a_n$ and $b_n$ are equivalent sequences and $a_n$ is bounded then so is $b_n$.Show that $s_n$ is bounded if $s_n = b_1r + b_2r^2 + … + b_nr^n$ and $0 < r < 1$.Implicit Fact about Bounded Monotone Sequence convergesBolzano-Weierstrass boundedProve that if a sequence is eventually bounded then it is bounded













2












$begingroup$


The title says it. Can a bounded number sequence be strictly ascending / descending?



I have a problem that tells me the sequence of fractional parts $(nx)_ngeq 1$ (where $x$ is given) is ascending. But I know that the sequence is bounded $[0,1)$. Thus, shouldn’t the sequence stop ascending at a point? Please show me a proof or something.






sequences-and-series







share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    A series deals with summation. A sequence deals with individual elements.
    $endgroup$
    – Subhasis Biswas
    11 hours ago






  • 4




    $begingroup$
    You've received two examples of a bounded sequence that is strictly increasing. But I'm questioning your premise. For a fixed $x$, the sequence $(nx)_nge1$ is never strictly increasing.
    $endgroup$
    – Teepeemm
    8 hours ago















2












$begingroup$


The title says it. Can a bounded number sequence be strictly ascending / descending?



I have a problem that tells me the sequence of fractional parts $(nx)_ngeq 1$ (where $x$ is given) is ascending. But I know that the sequence is bounded $[0,1)$. Thus, shouldn’t the sequence stop ascending at a point? Please show me a proof or something.






sequences-and-series







share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    A series deals with summation. A sequence deals with individual elements.
    $endgroup$
    – Subhasis Biswas
    11 hours ago






  • 4




    $begingroup$
    You've received two examples of a bounded sequence that is strictly increasing. But I'm questioning your premise. For a fixed $x$, the sequence $(nx)_nge1$ is never strictly increasing.
    $endgroup$
    – Teepeemm
    8 hours ago













2












2








2





$begingroup$


The title says it. Can a bounded number sequence be strictly ascending / descending?



I have a problem that tells me the sequence of fractional parts $(nx)_ngeq 1$ (where $x$ is given) is ascending. But I know that the sequence is bounded $[0,1)$. Thus, shouldn’t the sequence stop ascending at a point? Please show me a proof or something.






sequences-and-series







share|cite|improve this question











$endgroup$




The title says it. Can a bounded number sequence be strictly ascending / descending?



I have a problem that tells me the sequence of fractional parts $(nx)_ngeq 1$ (where $x$ is given) is ascending. But I know that the sequence is bounded $[0,1)$. Thus, shouldn’t the sequence stop ascending at a point? Please show me a proof or something.






sequences-and-series




sequences-and-series






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 11 hours ago







furfur

















asked 11 hours ago









furfurfurfur

699




699







  • 1




    $begingroup$
    A series deals with summation. A sequence deals with individual elements.
    $endgroup$
    – Subhasis Biswas
    11 hours ago






  • 4




    $begingroup$
    You've received two examples of a bounded sequence that is strictly increasing. But I'm questioning your premise. For a fixed $x$, the sequence $(nx)_nge1$ is never strictly increasing.
    $endgroup$
    – Teepeemm
    8 hours ago












  • 1




    $begingroup$
    A series deals with summation. A sequence deals with individual elements.
    $endgroup$
    – Subhasis Biswas
    11 hours ago






  • 4




    $begingroup$
    You've received two examples of a bounded sequence that is strictly increasing. But I'm questioning your premise. For a fixed $x$, the sequence $(nx)_nge1$ is never strictly increasing.
    $endgroup$
    – Teepeemm
    8 hours ago







1




1




$begingroup$
A series deals with summation. A sequence deals with individual elements.
$endgroup$
– Subhasis Biswas
11 hours ago




$begingroup$
A series deals with summation. A sequence deals with individual elements.
$endgroup$
– Subhasis Biswas
11 hours ago




4




4




$begingroup$
You've received two examples of a bounded sequence that is strictly increasing. But I'm questioning your premise. For a fixed $x$, the sequence $(nx)_nge1$ is never strictly increasing.
$endgroup$
– Teepeemm
8 hours ago




$begingroup$
You've received two examples of a bounded sequence that is strictly increasing. But I'm questioning your premise. For a fixed $x$, the sequence $(nx)_nge1$ is never strictly increasing.
$endgroup$
– Teepeemm
8 hours ago










3 Answers
3






active

oldest

votes


















21












$begingroup$


Can a bounded number sequence be strictly ascending?




Sure it can.



Hint



$0.9 ;,; 0.99 ;,; 0.999 ;,; ldots$






share|cite|improve this answer











$endgroup$




















    16












    $begingroup$

    I presume you mean sequence, not series. For example, the sequence $1 - 1/n$ is bounded and strictly increasing.






    share|cite|improve this answer









    $endgroup$




















      2












      $begingroup$

      Yes.



      Though the mathematic series is "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities,"



      So basically the sequence of the partial sums of e.g. a geometric series
      with rate r: 0<r<1 will be an ever increasing, bounded, number. Copy pasting wikipedia:



      enter image description here



      This is also the base for Zeno's Paradoxes






      share|cite|improve this answer









      $endgroup$












      • $begingroup$
        +1 for Zeno's paradox
        $endgroup$
        – Pere
        6 hours ago










      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      21












      $begingroup$


      Can a bounded number sequence be strictly ascending?




      Sure it can.



      Hint



      $0.9 ;,; 0.99 ;,; 0.999 ;,; ldots$






      share|cite|improve this answer











      $endgroup$

















        21












        $begingroup$


        Can a bounded number sequence be strictly ascending?




        Sure it can.



        Hint



        $0.9 ;,; 0.99 ;,; 0.999 ;,; ldots$






        share|cite|improve this answer











        $endgroup$















          21












          21








          21





          $begingroup$


          Can a bounded number sequence be strictly ascending?




          Sure it can.



          Hint



          $0.9 ;,; 0.99 ;,; 0.999 ;,; ldots$






          share|cite|improve this answer











          $endgroup$




          Can a bounded number sequence be strictly ascending?




          Sure it can.



          Hint



          $0.9 ;,; 0.99 ;,; 0.999 ;,; ldots$







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 5 hours ago

























          answered 11 hours ago









          StackTDStackTD

          23.5k2154




          23.5k2154





















              16












              $begingroup$

              I presume you mean sequence, not series. For example, the sequence $1 - 1/n$ is bounded and strictly increasing.






              share|cite|improve this answer









              $endgroup$

















                16












                $begingroup$

                I presume you mean sequence, not series. For example, the sequence $1 - 1/n$ is bounded and strictly increasing.






                share|cite|improve this answer









                $endgroup$















                  16












                  16








                  16





                  $begingroup$

                  I presume you mean sequence, not series. For example, the sequence $1 - 1/n$ is bounded and strictly increasing.






                  share|cite|improve this answer









                  $endgroup$



                  I presume you mean sequence, not series. For example, the sequence $1 - 1/n$ is bounded and strictly increasing.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 11 hours ago









                  Robert IsraelRobert Israel

                  327k23216470




                  327k23216470





















                      2












                      $begingroup$

                      Yes.



                      Though the mathematic series is "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities,"



                      So basically the sequence of the partial sums of e.g. a geometric series
                      with rate r: 0<r<1 will be an ever increasing, bounded, number. Copy pasting wikipedia:



                      enter image description here



                      This is also the base for Zeno's Paradoxes






                      share|cite|improve this answer









                      $endgroup$












                      • $begingroup$
                        +1 for Zeno's paradox
                        $endgroup$
                        – Pere
                        6 hours ago















                      2












                      $begingroup$

                      Yes.



                      Though the mathematic series is "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities,"



                      So basically the sequence of the partial sums of e.g. a geometric series
                      with rate r: 0<r<1 will be an ever increasing, bounded, number. Copy pasting wikipedia:



                      enter image description here



                      This is also the base for Zeno's Paradoxes






                      share|cite|improve this answer









                      $endgroup$












                      • $begingroup$
                        +1 for Zeno's paradox
                        $endgroup$
                        – Pere
                        6 hours ago













                      2












                      2








                      2





                      $begingroup$

                      Yes.



                      Though the mathematic series is "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities,"



                      So basically the sequence of the partial sums of e.g. a geometric series
                      with rate r: 0<r<1 will be an ever increasing, bounded, number. Copy pasting wikipedia:



                      enter image description here



                      This is also the base for Zeno's Paradoxes






                      share|cite|improve this answer









                      $endgroup$



                      Yes.



                      Though the mathematic series is "In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities,"



                      So basically the sequence of the partial sums of e.g. a geometric series
                      with rate r: 0<r<1 will be an ever increasing, bounded, number. Copy pasting wikipedia:



                      enter image description here



                      This is also the base for Zeno's Paradoxes







                      share|cite|improve this answer












                      share|cite|improve this answer



                      share|cite|improve this answer










                      answered 7 hours ago









                      ntgntg

                      1436




                      1436











                      • $begingroup$
                        +1 for Zeno's paradox
                        $endgroup$
                        – Pere
                        6 hours ago
















                      • $begingroup$
                        +1 for Zeno's paradox
                        $endgroup$
                        – Pere
                        6 hours ago















                      $begingroup$
                      +1 for Zeno's paradox
                      $endgroup$
                      – Pere
                      6 hours ago




                      $begingroup$
                      +1 for Zeno's paradox
                      $endgroup$
                      – Pere
                      6 hours ago

















                      draft saved

                      draft discarded
















































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