Sequence with infinite range and 3 accumulation points











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I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:



I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.



I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.



Am I right or I completely miss a point of task?






real-analysis sequences-and-series







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  • The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
    – steven gregory
    yesterday

















up vote
0
down vote

favorite












I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:



I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.



I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.



Am I right or I completely miss a point of task?






real-analysis sequences-and-series







share|cite|improve this question






















  • The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
    – steven gregory
    yesterday















up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:



I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.



I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.



Am I right or I completely miss a point of task?






real-analysis sequences-and-series







share|cite|improve this question













I have a task about limits and accumulation points, but I'm a little bit confused about it. The task is the following:



I'm asked to find a sequence with 3 accumulation points, but with an infinite range. Also, for each accumulation point, I should find a monotone subsequence converging to that point.



I have an assumption that such sequence can be described as Sn = {2, 1, 0, 4, 2, 1, 0, 6, 2, 1, 0, ...}
and the subsequences are like {4, 2, 1, 0}, {4, 2, 1}, {4, 2}, since 2, 1 and 0 are accumulation points.



Am I right or I completely miss a point of task?






real-analysis sequences-and-series




real-analysis sequences-and-series






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asked yesterday









Sergey Malinov

51




51












  • The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
    – steven gregory
    yesterday




















  • The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
    – steven gregory
    yesterday


















The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday






The subsequences will be ${4,4,4,4,dots}$, ${2,2,2,2,dots}$, and so on.
– steven gregory
yesterday












1 Answer
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Your accumulation points are correct.



Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,






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    1 Answer
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    1 Answer
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    active

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    active

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    up vote
    0
    down vote



    accepted










    Your accumulation points are correct.



    Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,






    share|cite|improve this answer

























      up vote
      0
      down vote



      accepted










      Your accumulation points are correct.



      Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,






      share|cite|improve this answer























        up vote
        0
        down vote



        accepted







        up vote
        0
        down vote



        accepted






        Your accumulation points are correct.



        Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,






        share|cite|improve this answer












        Your accumulation points are correct.



        Your sun sequences are the constant subsequences $$ 0,0,0,...$$,$$1,1,1,....$$ and $$2,2,2,.....$$,







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered yesterday









        Mohammad Riazi-Kermani

        40.2k41958




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