Timeline for Extracting a common convergent indexing from an uncountable family of sequences
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Dec 12, 2023 at 19:10 | history | suggested | Peter Mortensen | CC BY-SA 4.0 |
Removed historical information (that is what the revision history is for)βthe answer should be as if it was written right now; see e.g. <https://meta.stackexchange.com/a/131011>. Removed meta information (this belongs in comments).
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| Dec 12, 2023 at 19:03 | review | Suggested edits | |||
| S Dec 12, 2023 at 19:10 | |||||
| Dec 11, 2023 at 13:59 | comment | added | Farmer S | I put it in an answer below... | |
| Dec 11, 2023 at 13:51 | comment | added | Joel David Hamkins | And that idea will seem to work for separable Banach spaces also, because we can say 0/1 depending on whether you are within a rational distance of the $n$th point or not. If this is right, we have $π=π_{\mathbb{R}}=π_{\{0,1\}}=\frak{s}$. | |
| Dec 11, 2023 at 13:49 | comment | added | Joel David Hamkins | @FarmerS Could you clarify? I had some ideas in that direction, but didn't quite see it. I guess you want to replace each sequence with an omega sequence of 0/1 sequences, which give information about above/below a given rational target. If we can make those all converge, then the original sequence will also. | |
| Dec 11, 2023 at 13:41 | comment | added | Farmer S | Isn't $c_{\mathbb{R}}=c_{\{0,1\}}$, by approximating an $\mathbb{R}$-valued sequence with an $\omega$-sequence of $\{0,1\}$-valued sequences and diagonalizing to produce an index set giving common convergence? | |
| Dec 11, 2023 at 12:28 | comment | added | Joel David Hamkins | Fantastic! We seem to be converging on the common convergence number. | |
| Dec 11, 2023 at 11:17 | history | edited | alvoi | CC BY-SA 4.0 |
added 166 characters in body
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| Dec 11, 2023 at 9:40 | history | answered | alvoi | CC BY-SA 4.0 |