Timeline for Solving interval problems without outer measure
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 24, 2023 at 20:58 | review | Close votes | |||
| Aug 31, 2023 at 3:09 | |||||
| Aug 24, 2023 at 20:49 | comment | added | Ross Ure Anderson | I did not receive any responses on MSE, however I did receive a very helpful answer on here, which also provides a non-measure theory solution to a similar problem cited in this answer. And yes, compactness is used. By 'interval' I mean any kind of interval in $\mathbb{R}$, including unbounded. | |
| Aug 24, 2023 at 20:43 | comment | added | Nate Eldredge | One thing to consider is that your proof has to use the completeness of $\mathbb{R}$ in some form, since the statement is not true for $\mathbb{Q}$ (the unit interval in $\mathbb{Q}$ can be covered by a sequence of intervals whose total lengths are less than 1, or indeed arbitrarily small). The most common proofs use it via the fact that the unit interval in $\mathbb{R}$ is compact. But it means the proof has to be somehow "topological" and can't be done with pure arithmetic. | |
| Aug 24, 2023 at 20:39 | comment | added | Nate Eldredge | First question: when you say "interval", do you mean open, closed, half-open, what? | |
| Aug 24, 2023 at 20:38 | comment | added | Nate Eldredge | I think Math.SE is a better place for this question, since it's standard textbook material. | |
| Aug 24, 2023 at 19:42 | answer | added | Fedor Petrov | timeline score: 2 | |
| Aug 24, 2023 at 17:05 | history | edited | Ross Ure Anderson | CC BY-SA 4.0 |
added 343 characters in body
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| Aug 17, 2023 at 15:10 | answer | added | Ross Ure Anderson | timeline score: 1 | |
| Aug 17, 2023 at 12:46 | comment | added | ho boon suan | The answer at mathoverflow.net/a/51555 and its comments seem relevant to Problem 1. | |
| Aug 16, 2023 at 23:50 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Aug 16, 2023 at 22:28 | answer | added | Nik Weaver | timeline score: 5 | |
| Aug 16, 2023 at 21:47 | history | asked | Ross Ure Anderson | CC BY-SA 4.0 |