network profile
| bio | website | |
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| location | ||
| age | ||
| visits | member for | 11 months |
| seen | Jun 13 '12 at 20:39 | |
| stats | profile views | 5 |
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Jun 12 |
comment |
Limits of Subsequences Is there any exceptions where the result be not true? |
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Jun 12 |
comment |
Limits of Subsequences So the method of proof works also in the case if $s_{n}=t_{n},\forall n$, right! |
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Jun 12 |
awarded | Scholar |
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Jun 12 |
awarded | Commentator |
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Jun 12 |
accepted | Limits of Subsequences |
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Jun 12 |
comment |
Limits of Subsequences Oh ok, that's fine now, Thank you! |
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Jun 12 |
comment |
Limits of Subsequences Are you sure about the index of $s'_{n}$ in the last line above? |
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Jun 12 |
asked | Limits of Subsequences |
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Jun 12 |
comment |
Sequence space and limits Is it true the other way; given a sequence $s$, there is a sequence $s'$ such that $s\subset s'$ and $\lim s/s'=0$? |
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Jun 12 |
comment |
Sequence space and limits So is there any case where such sequence could exist? For example, any conditions on $S$ ? |
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Jun 12 |
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Sequence space and limits But I think at some point in the process of taking subsequences all the subsequences will behaves in a same rate, is it true? |
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Jun 12 |
comment |
Sequence space and limits Is it possible to multiply the ratio $\frac{s'}{s}$ by a fixed sequence $x_{n}$ converging to zero, not necessary from $S$, to make the problem true? |
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Jun 12 |
asked | Sequence space and limits |
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Jun 12 |
revised |
Set of sequences added 8 characters in body |
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Jun 12 |
revised |
Set of sequences added 79 characters in body |
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Jun 12 |
comment |
Set of sequences So, any help!!? |
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Jun 12 |
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Set of sequences It just came to my mind: if there is a sequence $\{s_{n}\}\in S$ which converges to 0 then there will be many such sequences in $S$ by taking subsequences of that $\{s_{n}\}$, which all will convereg to 0. |
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Jun 12 |
revised |
Set of sequences deleted 1 characters in body |
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Jun 12 |
revised |
Set of sequences added 100 characters in body |
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Jun 12 |
comment |
Set of sequences @Arturo: $\{h_{n}\}$ is any sequence of functions in $H$. So to make the definition clear, $S=\{\,\{s_{n}\}: s_{n}=\sup_{\mathbb R}|h_{n}(x)|, \{h_{n}\}\subset H, s_{n}\to 0\}$. |
