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When reading a set theorem, there is a part that:

  • Defined a sequence $S_{n}$.
  • Let $N = \inf\{n:S_{n}=0\}$ and let $X_{n} = S_{N \land n}$

I could not understand the operation $ \land$ in $S_{N \land n}$. Is this "and" operation? If it's true so what is it meaning of $S_{N \land n}$?

I hope someone can explain it to me. Thank you very much.

drhab
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M.bara
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    I suspect $N\wedge n=\min(n,N)$. In orders $p\wedge q$ is used to denote the largest lower bound of ${p,q}$. – drhab Jul 02 '20 at 07:12
  • @drhab: Thank you for your suggestion. Since the value of $N$ is scalar. If $N \land n = \min(n,N)$, the value of $X_{n}$ will equal to the value of $S_{n}$ while $n = 1 : N-1$. After that all the values of $X_{n}$ will be the same as $S_{N}$. Is that right? – M.bara Jul 02 '20 at 07:20
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    If $n<N$ then $X_n=S_{n\wedge N}=S_n\neq 0$. If $n\geq N$ then $X_n=S_{n\wedge N}=S_N=0$. – drhab Jul 02 '20 at 07:25
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    If you continue reading to the point where the author draws conclusions about the behavior of $X_n$, it might become clear what it's expected to mean. For that matter, it would help if you could quote or photograph the context in your question. – Chris Culter Jul 02 '20 at 07:27

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