Timeline for Is there order to the number of groups of different orders?
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2010 at 7:53 | answer | added | BS. | timeline score: 1 | |
| Oct 19, 2010 at 7:34 | answer | added | dvitek | timeline score: 2 | |
| Oct 19, 2010 at 7:29 | comment | added | S. Carnahan♦ | -1: too much soapbox. | |
| Oct 19, 2010 at 6:11 | answer | added | Greg Kuperberg | timeline score: 2 | |
| Oct 13, 2010 at 23:34 | comment | added | Gerry Myerson | A natural-though-not-exceedingly-informative statement is that if $m$ divides $n$ then $f(m)\le f(n)$. | |
| Oct 13, 2010 at 21:59 | comment | added | Michael Lugo | The behavior of the function $F: \mathbb{N}^\infty \to \mathbb{N}$, where $F(x_2, x_3, x_5, x_7, \ldots) = f(2^{x_2} 3^{x_3} 5^{x_5} 7^{x_7} \ldots)$, is perhaps less erratic. (In other words, $f(n)$ really depends on the prime factorization of $n$.) | |
| Oct 13, 2010 at 19:37 | comment | added | Ben Webster♦ | Of course, f only seems erratic if you think about numbers sequentially, as opposed to in terms of divisibility. | |
| Oct 13, 2010 at 19:22 | comment | added | Yemon Choi | What's unnatural about the prime number theorem? | |
| Oct 13, 2010 at 19:20 | comment | added | Autumn Kent | I didn't know that dimension was unnatural. | |
| Oct 13, 2010 at 18:52 | comment | added | James D. Taylor | It's unnatural in the sense that it doesn't explain the error terms. If you look at an algebro-geometric object "generically" - you have a geometric idea of why there are errors. But I feel that asymptotic arguments tend to bunch all the errors together and throw them in the nobody-cares pile. Surely, it has benefits. But certainly you can see it's arguably unnatural. | |
| Oct 13, 2010 at 18:36 | comment | added | Qiaochu Yuan | In what way are asymptotic statements inherently unnatural? Asymptotics are an important way of ignoring extraneous information in a problem to concentrate on the most important aspects of it, and arguably the whole realm of infinitary analysis is just about what happens when you focus only on the asymptotics (as epsilon goes to zero) and ignore the error terms. | |
| Oct 13, 2010 at 18:31 | history | edited | Noah Stein | CC BY-SA 2.5 |
added 35 characters in body
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| Oct 13, 2010 at 18:23 | history | asked | James D. Taylor | CC BY-SA 2.5 |