Timeline for Does every strictly increasing, unbounded sequence of positive real numbers contain arbitrarily long, finite subsequences which are "sort of increasing" or "sort of decreasing" (as defined below)?
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5 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2023 at 10:00 | comment | added | Pietro Majer | Unless I misunderstand the definition of "(M,N)-expander" this seems to me a counterexample (it could be made more explicit). There exists an increasing unbounded sequence $(x_n)_n$ all of whose sub-subsequences must have both unbounded and infinitesimal ratios $\frac{x_{i(n+1)}-x_{i(n)}}{x_{i(m+1)}-x_{i(m)}}$, for $m<n$. | |
| Feb 20, 2015 at 2:08 | comment | added | The Masked Avenger | Nice example. As I understand things, one can switch to having very large or very small ratios, and it can began with any term. I do not see this as a counterexample. I recommend leaving it as a source to inspire others. | |
| Feb 19, 2015 at 16:46 | review | Late answers | |||
| Feb 19, 2015 at 16:53 | |||||
| Feb 19, 2015 at 16:36 | review | First posts | |||
| Feb 19, 2015 at 16:43 | |||||
| Feb 19, 2015 at 16:29 | history | answered | Neil Maneck | CC BY-SA 3.0 |