Timeline for What sets are known to have cardinality equal to $\mathbb{N}$ or $\mathbb{R}$ but open as to which?
Current License: CC BY-SA 4.0
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| Sep 27, 2023 at 14:07 | comment | added | Sidharth Ghoshal | @FrançoisG.Dorais yea that seems like a perfect match, it looks like we also have made enough progress to know its independent of ZFC as opposed to merely being an open problem | |
| Sep 26, 2023 at 23:13 | comment | added | François G. Dorais | Borel's conjecture on Strong Measure Zero Sets comes to mind. Is that the kind of answer you want? | |
| Sep 26, 2023 at 22:41 | comment | added | Sidharth Ghoshal | I have updated the sentence to something hopefully a little clearer | |
| Sep 26, 2023 at 22:41 | history | edited | Sidharth Ghoshal | CC BY-SA 4.0 |
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| Sep 26, 2023 at 22:17 | comment | added | Daniel Asimov | The sentence "There are many sets which we do not know to be either finite or infinitely countable but do know it’s one of the two" contradicts itself. | |
| Sep 26, 2023 at 19:22 | history | edited | Stefan Kohl♦ |
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| Sep 26, 2023 at 19:21 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Sep 26, 2023 at 16:48 | history | edited | YCor |
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| Sep 26, 2023 at 15:30 | comment | added | Mikhail Katz | The number of twin hypernatural primes. | |
| Sep 26, 2023 at 15:05 | review | Close votes | |||
| Oct 2, 2023 at 3:04 | |||||
| Sep 26, 2023 at 15:00 | comment | added | Sidharth Ghoshal | I have edited my post to reflect the earlier question had a similar spirit but was not the same | |
| Sep 26, 2023 at 14:58 | history | edited | Sidharth Ghoshal | CC BY-SA 4.0 |
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| Sep 26, 2023 at 14:57 | comment | added | Sam Hopkins | @SidharthGhoshal: but then this is not at all "the same question" as the one you link to on MSE. | |
| Sep 26, 2023 at 14:51 | comment | added | Sidharth Ghoshal | I have clarified the question, when I had written “countable” earlier I meant “countably infinite” or “cardinality of the natural numbers”. Similarly when I had written uncountable earlier I meant “cardinality of the continuum” | |
| Sep 26, 2023 at 14:49 | history | edited | Sidharth Ghoshal | CC BY-SA 4.0 |
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| Sep 26, 2023 at 14:41 | comment | added | GH from MO | Your title is about the cardinality of $\mathbb{N}$ vs. the cardinality of $\mathbb{R}$, while your main text is about "countable vs. uncountable". These are not the same thing, so please clarify your question. | |
| Sep 26, 2023 at 14:29 | comment | added | Emil Jeřábek | $\mathbb N\cup\{x\in\mathbb R:\text{the Riemann hypothesis holds}\}$. | |
| Sep 26, 2023 at 14:27 | comment | added | YCor | Non-natural example: the closure in $\mathbf{Z}_p$ of the union of the set of twin primes. | |
| Sep 26, 2023 at 14:24 | history | asked | Sidharth Ghoshal | CC BY-SA 4.0 |