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

UART pins to unpowered MCU?

Compression function is not collision resistant but Merkle-Damgard is collision resistant

Set and print content of environment variable in cmd.exe subshell?

Single word request: Harming the benefactor

Aliens englobed the Solar System: will we notice?

Finding algorithms of QGIS commands?

Reverse string, can I make it faster?

Virginia employer terminated employee and wants signing bonus returned

Why the color red for the Republican Party

Replacing Windows 7 security updates with 3rd party alternatives?

How to pass a string to a command that expects a file?

What are actual Tesla M60 models used by AWS?

What Happens when Passenger Refuses to Fly Boeing 737 Max?

Grey hair or white hair

How can The Temple of Elementary Evil reliably protect itself against kinetic bombardment?

Meaning of ちはース as an exclamation

Is there any way to click on 6th item of this list

Numbering Question Help Me!

How can I ensure my trip to the UK will not have to be cancelled because of Brexit?

How to create a hard link to an inode (ext4)?

Is there an equal sign with wider gap?

Accepted offer letter, position changed

They call me Inspector Morse

Do any of the books contain (magic) items for animal companions?



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













1












$begingroup$


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











$endgroup$











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















1












$begingroup$


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











$endgroup$











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













1












1








1





$begingroup$


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 2 hours ago







furfur

















asked 2 hours ago









furfurfurfur

619




619











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
















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















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




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










2 Answers
2






active

oldest

votes


















6












$begingroup$

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






share|cite|improve this answer









$endgroup$




















    6












    $begingroup$

    Sure it can.



    Hint



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






    share|cite|improve this answer









    $endgroup$












      Your Answer





      StackExchange.ifUsing("editor", function ()
      return StackExchange.using("mathjaxEditing", function ()
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      );
      );
      , "mathjax-editing");

      StackExchange.ready(function()
      var channelOptions =
      tags: "".split(" "),
      id: "69"
      ;
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function()
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled)
      StackExchange.using("snippets", function()
      createEditor();
      );

      else
      createEditor();

      );

      function createEditor()
      StackExchange.prepareEditor(
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader:
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      ,
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      );



      );













      draft saved

      draft discarded


















      StackExchange.ready(
      function ()
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3145023%2fcan-a-bounded-number-sequence-be-strictly-ascending%23new-answer', 'question_page');

      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      6












      $begingroup$

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






      share|cite|improve this answer









      $endgroup$

















        6












        $begingroup$

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






        share|cite|improve this answer









        $endgroup$















          6












          6








          6





          $begingroup$

          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 2 hours ago









          Robert IsraelRobert Israel

          327k23216469




          327k23216469





















              6












              $begingroup$

              Sure it can.



              Hint



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






              share|cite|improve this answer









              $endgroup$

















                6












                $begingroup$

                Sure it can.



                Hint



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






                share|cite|improve this answer









                $endgroup$















                  6












                  6








                  6





                  $begingroup$

                  Sure it can.



                  Hint



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






                  share|cite|improve this answer









                  $endgroup$



                  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










                  answered 2 hours ago









                  StackTDStackTD

                  23.4k2153




                  23.4k2153



























                      draft saved

                      draft discarded
















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …


                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.

                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function ()
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3145023%2fcan-a-bounded-number-sequence-be-strictly-ascending%23new-answer', 'question_page');

                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -sequences-and-series
                      -

                      Popular posts from this blog

                      Creating 100m^2 grid automatically using QGIS?Creating grid constrained within polygon in QGIS?Createing polygon layer from point data using QGIS?Creating vector grid using QGIS?Creating grid polygons from coordinates using R or PythonCreating grid from spatio temporal point data?Creating fields in attributes table using other layers using QGISCreate .shp vector grid in QGISQGIS Creating 4km point grid within polygonsCreate a vector grid over a raster layerVector Grid Creates just one grid

                      Image
                      Pattern match does not work in bash script Mage Armor with Defense fighting style (for Adventurers League bladeslinger) LaTeX closing $ signs makes cursor jump String Manipulation Interpreter Can divisibility rules for digits be generalized to sum of digits I'm planning on buying a laser printer but concerned about the life cycle of toner in the machine What is the offset in a seaplane's hull? How can I make my BBEG immortal short of making them a Lich or Vampire? What are the differences between the usage of 'it' and 'they'? The use of multiple foreign keys on same column in SQL Server How did the USSR manage to innovate in an environment characterized by government censorship and high bureaucracy? Is it tax fraud for an individual to declare non-taxable revenue as taxable income? (US tax laws) Why Is Death Allowed In the Matrix? Minkowski space Why are 150k or 200k jobs considered good when there are 300k+ births a month? Why do f...
                      Read more

                      Word for a person who has no opinion about whether god existsWord for having a definite opinion while simultaneously withholding judgment?What's the opposite of “newcomer? Is ”veteran" OK?What do you call an “atheist” who might believe in an afterlife?What's a word for someone who wants to voice opinions but not have them challenged?Word for someone who dismisses contrary opinions as irrational?Somone who thinks they are overly special/out of the ordinaryIs there a word, phrase or idiom for “a person who is incapable of thinking about the future”?The belief that a god is human-likeA word for a non-famous person/thing you have heard a lot aboutAdjective for a person who enjoys taking care of their appearance

                      Image
                      Reverse string, can I make it faster? How strictly should I take "Candidates must be local"? Are there historical instances of the capital of a colonising country being temporarily or permanently shifted to one of its colonies? Accepted offer letter, position changed Could you please stop shuffling the deck and play already? How to secure an aircraft at a transient parking space? At what distance can a bugbear, holding a reach weapon, with the Polearm Master feat, get their Opportunity Attack? Why was Goose renamed from Chewie for the Captain Marvel film? Is it necessary to separate DC power cables and data cables? Is "history" a male-biased word ("his+story")? Why the color red for the Republican Party What's wrong with this bogus proof? Doesn't allowing a user mode program to access kernel space memory and execute the IN and OUT instructions defeat the purpose of having CPU modes? Can one live in the U.S. and not use a c...
                      Read more

                      Can I redirect output to a log file and background a process at the same time?2019 Community Moderator ElectionUnable to write to file in shell script when running command in backgroundredirect and log script outputhow to properly log the output of a console program that frequently updates “parts” of the screen, resulting in a messy log file?How can I redirect the output of a child process?grep script - output lines at the same time into echoHow to run process in background and get its pid to create log file nameHow to redirect output to a log from expect commandHow to clear a redirect log file content in shell?Log background jobs started in all the manually started shells?Why do `jobs` and `dirs` run in command subsitution, process substitution, pipeline, and background jobs output the same as in original shell?How to redirect output to file to STDOUT?

                      Image
                      Makefile strange variable substitution Are all players supposed to be able to see each others' character sheets? How to draw cubes in a 3 dimensional plane Shifting between bemols (flats) and diesis (sharps)in the key signature They call me Inspector Morse An alternative proof of an application of Hahn-Banach Virginia employer terminated employee and wants signing bonus returned Why was Goose renamed from Chewie for the Captain Marvel film? Accepted offer letter, position changed Why does Captain Marvel assume the people on this planet know this? Word for a person who has no opinion about whether god exists Are babies of evil humanoid species inherently evil? How do I express some one as a black person? Am I not good enough for you? Does the nature of the Apocalypse in The Umbrella Academy change from the first to the last episode? Definition of Statistic What problems would a superhuman have whose skin is constantly hot? meaning and function of ...
                      Read more