Timeline for Are there Generalisations of a Limit (for Just-divergent Sequences)?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2010 at 19:47 | comment | added | Rhubbarb | Thanks for this reply. Any additional information and any additional ideas are appreciated. | |
| Feb 5, 2010 at 3:33 | comment | added | Matt Noonan | If I'm understanding it correctly, this technique subsumes some of the other limits mentioned, such as the one in the original question. Statistics of the distribution can give various limit notions. Seems like an interesting approach! | |
| Feb 5, 2010 at 1:33 | comment | added | user3035 | The connection is that this gives a different and (depending on the application) potentially useful way to characterize a sequence and its limiting behavior. | |
| Feb 5, 2010 at 1:32 | comment | added | user3035 | The question (specifically the part that said "Are there other ways to define such a thing") was, are there any ways to talk about and define sequence convergence, other than the standard definition from freshman calculus. My response is, look at the distribution of the values of the sequence and see if that distribution can be characterized somehow. For example, if the sequence is $a_n = (-1)^n$, then the distribution of its values is peaked at two points, +1 and -1. For a sequence $a_n = \sin(n)$, the distribution is different (covering almost uniformly much of $[-1, 1]$). | |
| Feb 4, 2010 at 21:29 | comment | added | Yemon Choi | I'm afraid I don't really see the connection; and as many other comments have noted, there is a well-established body of techniques to handle divergent series, which seem more relevant to the question at hand. | |
| Feb 4, 2010 at 21:23 | history | answered | user3035 | CC BY-SA 2.5 |