Timeline for Independence result where probabilistic intuition predicts the wrong answer?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2021 at 14:36 | vote | accept | Timothy Chow | ||
| Jan 19, 2021 at 9:59 | comment | added | Monroe Eskew | I think the way the question is framed is a bit misleading. There is not just one “meaning” of generic that is close to comeagerness. “Generic” has only a technical meaning in terms of a partial order and a collection of dense subsets of it. It can correspond to comeagerness, or Lebesgue measure one, or these notions relativized to some other topology or measure, or “measure one” for some other ideal like the Marczewski ideal, or generic with respect to ideals on higher Baire space, or a generic closed subset of a stationary set, etc. etc. | |
| Jan 19, 2021 at 7:01 | history | became hot network question | |||
| Jan 19, 2021 at 6:24 | comment | added | Anthony Quas | Hmmm so I'm not sure about the set-theoretic independence part, but in case it's relevant, the set $A=\{x\in[0,1]\colon \exists \text{infinitely many }p,q\text{ such that }|x-\frac pq|<\frac{1}{q^3}\}$ is an easily understandable residual set of measure 0. | |
| Jan 19, 2021 at 5:40 | comment | added | Timothy Chow | @AnthonyQuas : Yes, I mean set-theoretic independence. | |
| Jan 19, 2021 at 5:25 | comment | added | Anthony Quas | Sorry to be dumb here, but what do you mean by an independence result? Are we talking about set-theoretic independence here? | |
| Jan 19, 2021 at 2:23 | answer | added | Andreas Blass | timeline score: 10 | |
| Jan 18, 2021 at 23:59 | answer | added | Buzz | timeline score: 1 | |
| Jan 18, 2021 at 23:12 | comment | added | Asaf Karagila♦ | Take a meager co-null set (e.g. the union of fat Cantor sets with measures approaching to $1$), then adding a Cohen real would avoid this set. Now take some "natural description of a Cohen real" and make that into your wanted example. | |
| Jan 18, 2021 at 23:01 | history | asked | Timothy Chow | CC BY-SA 4.0 |