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 Nov 17 at 12:55


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  • 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
    Nov 17 at 8:45















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















marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 Nov 17 at 12:55


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
    Nov 17 at 8:45













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
















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















share|cite|improve this question













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edited Nov 17 at 9:34









Brahadeesh

5,54841956




5,54841956










asked Nov 17 at 8:40









Sashin Chetty

172




172




marked as duplicate by Brahadeesh, drhab, Hans Lundmark, Lord Shark the Unknown, user10354138 Nov 17 at 12:55


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 Nov 17 at 12:55


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
    Nov 17 at 8:45


















  • 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
    Nov 17 at 8:45
















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
Nov 17 at 8:45




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
Nov 17 at 8:45










2 Answers
2






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up vote
7
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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.






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  • 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
    Nov 17 at 8:47




















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
      Nov 17 at 8:47

















    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
      Nov 17 at 8:47















    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 Nov 17 at 8:43









    Joey Kilpatrick

    1,163121




    1,163121








    • 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
      Nov 17 at 8:47
















    • 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
      Nov 17 at 8:47










    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
    Nov 17 at 8:47






    +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
    Nov 17 at 8:47












    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 Nov 17 at 10:33









        GuySa

        416313




        416313















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