Sequence Converging [on hold]

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Explain exactly what it means for $a_n$ $ninmathbb N$ to converge to $L ∈ R.$



Can someone please break down this question for me?




calculus sequences-and-series limits




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put on hold as off-topic by Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128
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    Can you edit your question to include the definition you are using, and what you don't understand about the definition?
    – quasi
    2 days ago











  • I'm voting to close this question until quasi's comment receives an appropriate answer.
    – Arnaud Mortier
    2 days ago










  • Please study our guide to new askers. You shoulld then understand why your question was not well received, and can take action.
    – Jyrki Lahtonen
    2 days ago














up vote
-3
down vote

favorite












Explain exactly what it means for $a_n$ $ninmathbb N$ to converge to $L ∈ R.$



Can someone please break down this question for me?




calculus sequences-and-series limits




share|cite|improve this question













put on hold as off-topic by Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 5




    Can you edit your question to include the definition you are using, and what you don't understand about the definition?
    – quasi
    2 days ago











  • I'm voting to close this question until quasi's comment receives an appropriate answer.
    – Arnaud Mortier
    2 days ago










  • Please study our guide to new askers. You shoulld then understand why your question was not well received, and can take action.
    – Jyrki Lahtonen
    2 days ago












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











Explain exactly what it means for $a_n$ $ninmathbb N$ to converge to $L ∈ R.$



Can someone please break down this question for me?




calculus sequences-and-series limits




share|cite|improve this question













Explain exactly what it means for $a_n$ $ninmathbb N$ to converge to $L ∈ R.$



Can someone please break down this question for me?





calculus sequences-and-series limits





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Michael Hardy

204k23185460




204k23185460









asked 2 days ago









Okie

395




395




put on hold as off-topic by Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Henrik, José Carlos Santos, amWhy, Arnaud Mortier, user 108128
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 5




    Can you edit your question to include the definition you are using, and what you don't understand about the definition?
    – quasi
    2 days ago











  • I'm voting to close this question until quasi's comment receives an appropriate answer.
    – Arnaud Mortier
    2 days ago










  • Please study our guide to new askers. You shoulld then understand why your question was not well received, and can take action.
    – Jyrki Lahtonen
    2 days ago












  • 5




    Can you edit your question to include the definition you are using, and what you don't understand about the definition?
    – quasi
    2 days ago











  • I'm voting to close this question until quasi's comment receives an appropriate answer.
    – Arnaud Mortier
    2 days ago










  • Please study our guide to new askers. You shoulld then understand why your question was not well received, and can take action.
    – Jyrki Lahtonen
    2 days ago







5




5




Can you edit your question to include the definition you are using, and what you don't understand about the definition?
– quasi
2 days ago





Can you edit your question to include the definition you are using, and what you don't understand about the definition?
– quasi
2 days ago













I'm voting to close this question until quasi's comment receives an appropriate answer.
– Arnaud Mortier
2 days ago




I'm voting to close this question until quasi's comment receives an appropriate answer.
– Arnaud Mortier
2 days ago












Please study our guide to new askers. You shoulld then understand why your question was not well received, and can take action.
– Jyrki Lahtonen
2 days ago




Please study our guide to new askers. You shoulld then understand why your question was not well received, and can take action.
– Jyrki Lahtonen
2 days ago










1 Answer
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0
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The definition says the following:
$forallepsilon>0$ $exists n_0in mathbbN$ $forall ngeq n_0$ $[|a_n-L|<epsilon]$



Take any positive number $epsilon$, doesn't matter how small it is. There must be an index $n_0 in mathbbN$ that starting from it the distance of all of the elements in the sequence from $L$ is smaller than $epsilon$. Of course the index $n_0$ depends on $epsilon$.






share|cite|improve this answer




























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    down vote













    The definition says the following:
    $forallepsilon>0$ $exists n_0in mathbbN$ $forall ngeq n_0$ $[|a_n-L|<epsilon]$



    Take any positive number $epsilon$, doesn't matter how small it is. There must be an index $n_0 in mathbbN$ that starting from it the distance of all of the elements in the sequence from $L$ is smaller than $epsilon$. Of course the index $n_0$ depends on $epsilon$.






    share|cite|improve this answer

























      up vote
      0
      down vote













      The definition says the following:
      $forallepsilon>0$ $exists n_0in mathbbN$ $forall ngeq n_0$ $[|a_n-L|<epsilon]$



      Take any positive number $epsilon$, doesn't matter how small it is. There must be an index $n_0 in mathbbN$ that starting from it the distance of all of the elements in the sequence from $L$ is smaller than $epsilon$. Of course the index $n_0$ depends on $epsilon$.






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        The definition says the following:
        $forallepsilon>0$ $exists n_0in mathbbN$ $forall ngeq n_0$ $[|a_n-L|<epsilon]$



        Take any positive number $epsilon$, doesn't matter how small it is. There must be an index $n_0 in mathbbN$ that starting from it the distance of all of the elements in the sequence from $L$ is smaller than $epsilon$. Of course the index $n_0$ depends on $epsilon$.






        share|cite|improve this answer













        The definition says the following:
        $forallepsilon>0$ $exists n_0in mathbbN$ $forall ngeq n_0$ $[|a_n-L|<epsilon]$



        Take any positive number $epsilon$, doesn't matter how small it is. There must be an index $n_0 in mathbbN$ that starting from it the distance of all of the elements in the sequence from $L$ is smaller than $epsilon$. Of course the index $n_0$ depends on $epsilon$.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered 2 days ago









        Mark

        5849




        5849












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