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My question is:

Is the vector space containing all periodic complex sequences a finite-dimensional vector space?

  • 2
    Consider $e^{(k)}$ the sequence defined by $e^{(k)}_k=1$ and $e^{(k)}_j=0$ for $k\neq j$. Now take $v_p:=\sum_{k=0}^{+\infty}e^{(kp)}$. These sequences are periodic.2011-10-09

2 Answers 2