Timeline for Image-catching families in $\omega$
Current License: CC BY-SA 4.0
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9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 29, 2024 at 8:21 | vote | accept | Dominic van der Zypen | ||
| Jul 28, 2024 at 7:24 | comment | added | Monroe Eskew | Oops, I read poorly. | |
| Jul 27, 2024 at 20:08 | comment | added | Michael Hardy |
@FarmerS Proper notation is either $\mathcal P(\omega)\setminus\{X\}$ or $\mathcal P(\omega)\smallsetminus\{X\}$ or maybe even $\mathcal P(\omega)-\{X\}.$ But \backslash doesn't give you the horizontal spacing appropriate to a binary relation symbol. It's as if you wrote $3{+}5$ instead of $3+5.$
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| Jul 27, 2024 at 13:39 | comment | added | Farmer S | But it only asks for there to be some C in the family such that $\varphi``C$ is in the family, not that the family be closed under this. | |
| Jul 27, 2024 at 13:22 | comment | added | Monroe Eskew | @FarmerS Hmm. If $\varphi$ is such that $\varphi[\neg X] = X$, then $\varphi[\neg X] \notin \mathcal P(\omega)\setminus \{X\}$. | |
| Jul 27, 2024 at 13:19 | answer | added | Farmer S | timeline score: 8 | |
| Jul 27, 2024 at 12:49 | comment | added | Farmer S | @MonroeEskew Why does that answer the question? E.g. if $X\subseteq\omega$ is infinite co-infinite, then $\mathcal{P}(\omega)\backslash\{X\}$ is image-catching. | |
| Jul 27, 2024 at 11:48 | comment | added | Monroe Eskew | Every countably infinite set is the bijective image of every other. | |
| Jul 26, 2024 at 21:33 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |