Timeline for Cofinality of infinitesimals
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2020 at 22:39 | history | became hot network question | |||
| Mar 29, 2020 at 16:44 | answer | added | Andreas Blass | timeline score: 8 | |
| Mar 29, 2020 at 15:07 | comment | added | Monroe Eskew | @JamesHanson Right. | |
| Mar 29, 2020 at 15:02 | comment | added | James E Hanson | It should be the cofinality of the reverse order on $(\omega^{\kappa}/U) \setminus \omega$, right? Not that that necessarily makes the question easier. | |
| Mar 29, 2020 at 14:56 | comment | added | Monroe Eskew | The thing is I am looking at increasing sequences of infinitesimals, i.e. converging to the gap. So if we take $1/\varepsilon$, then we are looking a decreasing sequence of infinite numbers. | |
| Mar 29, 2020 at 14:54 | comment | added | Asaf Karagila♦ | Well, if you look at $1/\varepsilon$, then you're looking at the cofinality of the linear order $\Bbb R^\kappa/U$, so the fact they are infinitesimals is irrelevant here. | |
| Mar 29, 2020 at 14:52 | comment | added | Monroe Eskew | @AsafKaragila This is the answer if we are looking at the set of things below a fixed element $[f]_U$, since for each $\alpha$ can choose a cofinal $\omega$-sequence in $f(\alpha)$. But there is no supremum to the set of infinitesimals, so basically I am asking about possible “gaps.” | |
| Mar 29, 2020 at 14:43 | comment | added | Asaf Karagila♦ | I imagine it's the cofinality of $\omega^\kappa/U$, as a linear order. | |
| Mar 29, 2020 at 14:31 | history | asked | Monroe Eskew | CC BY-SA 4.0 |