Can a sequence be undefined at a point? [duplicate]











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  • Are undefined terms allowed in a sequence?

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A sequence which is a mapping from $mathbb{N} to mathbb{R}$.



For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?






real-analysis sequences-and-series







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marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 2 days ago


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    2 days ago















up vote
2
down vote

favorite













This question already has an answer here:




  • Are undefined terms allowed in a sequence?

    3 answers




A sequence which is a mapping from $mathbb{N} to mathbb{R}$.



For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?






real-analysis sequences-and-series







share|cite|improve this question









New contributor




Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 2 days ago


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    2 days ago













up vote
2
down vote

favorite









up vote
2
down vote

favorite












This question already has an answer here:




  • Are undefined terms allowed in a sequence?

    3 answers




A sequence which is a mapping from $mathbb{N} to mathbb{R}$.



For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?






real-analysis sequences-and-series







share|cite|improve this question









New contributor




Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












This question already has an answer here:




  • Are undefined terms allowed in a sequence?

    3 answers




A sequence which is a mapping from $mathbb{N} to mathbb{R}$.



For example can the sequence ${a_n} = 1/(3-n)$.
This would be undefined at $3$.
Is it a sequence?





This question already has an answer here:




  • Are undefined terms allowed in a sequence?

    3 answers







real-analysis sequences-and-series




real-analysis sequences-and-series






share|cite|improve this question









New contributor




Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











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Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




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edited 2 days ago









Brahadeesh

5,52941956




5,52941956






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Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 2 days ago









Sashin Chetty

91




91




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Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Sashin Chetty is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 2 days ago


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 2 days ago


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    2 days ago


















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    2 days ago
















Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
2 days ago




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
2 days ago










2 Answers
2






active

oldest

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up vote
7
down vote













If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.






share|cite|improve this answer

















  • 2




    +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
    – Dave L. Renfro
    2 days ago




















up vote
1
down vote













If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:



$frac{1}{2}, 1, infty,-1, frac{-1}{2},...$



Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.






share|cite|improve this answer




























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    7
    down vote













    If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.






    share|cite|improve this answer

















    • 2




      +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
      – Dave L. Renfro
      2 days ago

















    up vote
    7
    down vote













    If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.






    share|cite|improve this answer

















    • 2




      +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
      – Dave L. Renfro
      2 days ago















    up vote
    7
    down vote










    up vote
    7
    down vote









    If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.






    share|cite|improve this answer












    If you define a sequence as a mapping $f$ from $Bbb N$ to $Bbb R$, then no, a sequence cannot be undefined at a point $x$, since if $f(x)$ was not defined, then $f$ isn't a mapping.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 2 days ago









    Joey Kilpatrick

    1,014121




    1,014121








    • 2




      +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
      – Dave L. Renfro
      2 days ago
















    • 2




      +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
      – Dave L. Renfro
      2 days ago










    2




    2




    +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
    – Dave L. Renfro
    2 days ago






    +1 for "just the facts", which is about all one can do unless the OP provides more information or context for the question. I was trying to write a comment about how $frac{1}{3-n}$ certainly defines a sequence if we begin with $n=4$ or later, and how the same infinite list of numbers can have different functions showing they're sequences, then started to trip over too many things, after which I pretty much decided to give it a pass, and then your answer showed up.
    – Dave L. Renfro
    2 days ago












    up vote
    1
    down vote













    If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:



    $frac{1}{2}, 1, infty,-1, frac{-1}{2},...$



    Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.






    share|cite|improve this answer

























      up vote
      1
      down vote













      If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:



      $frac{1}{2}, 1, infty,-1, frac{-1}{2},...$



      Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.






      share|cite|improve this answer























        up vote
        1
        down vote










        up vote
        1
        down vote









        If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:



        $frac{1}{2}, 1, infty,-1, frac{-1}{2},...$



        Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.






        share|cite|improve this answer












        If it's a sequence of real numbers, then go ahead and start noting the first few terms. In your case it will be:



        $frac{1}{2}, 1, infty,-1, frac{-1}{2},...$



        Is that really a sequence of real numbers? I'd say no, because $infty$ is not a real number.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 2 days ago









        GuySa

        414313




        414313















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