Timeline for Can a weaker version of the Hausdorff paradox be proved without AC?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2017 at 6:46 | comment | added | Andrej Bauer | I disagree with @bof. | |
| Mar 29, 2017 at 2:28 | comment | added | bof | $\aleph_0+\aleph_0=\aleph_0$ is a weaker (but still incredibly counterintuitive) version of the Hausdorff paradox which can be proved without AC. | |
| Mar 28, 2017 at 21:51 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 26, 2017 at 21:11 | answer | added | Julian Newman | timeline score: 2 | |
| Feb 26, 2017 at 3:57 | comment | added | user44143 | Yes to the second question, by A = {(cos(n), sin(n), 0): n in N}, let S = clockwise rotation by 1 radian. | |
| Feb 26, 2017 at 0:50 | comment | added | Simon Henry | With only ZF+DC, it is consistent that everything is measurable, so you cannot have identity of that sort that break "conservation of measure". But what you are asking is probably possible as one can take $A$ to have zero measure. for example, take a faithful action of the free group $F_2$ on the sphere, pick a point $p$ which is not a fixed point of any element of $F_2$, then the orbit of $p$ is isomorphic as a $F_2$ set to $F_2$ itself, and hence you are going to be able to find inside the orbit something very close to what you are asking using a paradoxical decomposition of $F_2$ | |
| Feb 26, 2017 at 0:04 | history | asked | Julian Newman | CC BY-SA 3.0 |