Timeline for An equivalent of the axiom of choice? [closed]
Current License: CC BY-SA 4.0
21 events
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| Nov 29, 2023 at 5:55 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Nov 27, 2023 at 4:07 | comment | added | bof | @AsafKaragila The OP further confuses the issue by changing the problem to "no one will try to escape unless it is impossible that he or she or they will be shot." In that case no well-ordering or AC is needed; all the guard has to say is "if any of you try to escape I'm going to kill one of you." Only one choice has to be made. | |
| Nov 27, 2023 at 4:03 | comment | added | bof | @AsafKaragila OK, if you assume (or the prisoners assume) that the guard is a sure shot, he never misses, his gun never jams, he can even pick out the lowest-numbered guy out of the trillions of escaping prisoners. The trouble with story problems is that mathematicians seldom take the trouble to make their stories make sense, or to state their assumptions explicitly as they would in a straignt mathematical problem. | |
| Nov 27, 2023 at 0:59 | comment | added | bof | OK. You confused the issue by changing "If a murderer is certain of death, he will not attempt to escape" to "no one will try to escape unless it is impossible that he or she or they will be shot." Even the original puzzle seems to require the unstated assumption that the guard is sure to hit his intended target. | |
| Nov 26, 2023 at 23:19 | comment | added | Michael Hardy | @bof : The prisoners are assigned (ordinal) numbers. A group may conspire to run away simultaneously, thinking that each of them has a chance of survival since only one will be shot. But they have been notified that in such an event, the one with the lowest number (well ordering) will be shot. Thus the one with the lowest number among the conspirators drops out. Then the one with the lowest number among those remaining drops out. And so on. | |
| Nov 26, 2023 at 16:32 | comment | added | Asaf Karagila♦ | @bof: You declare that any set of prisoners that escape, the one with the least number is gonna get shot. This guarantees that 0 is not escaping, and more generally, if nobody escapes with index less than $n$, then $n$ is not escaping either. So by (transfinite) induction, no well-orderable set of prisoners is going to escape. | |
| Nov 26, 2023 at 12:06 | comment | added | bof | How does a well-ordering solve the problem? | |
| Nov 26, 2023 at 0:01 | comment | added | Gerry Myerson | I found the 100 murderers question on some websites about quant job interviews. | |
| Nov 25, 2023 at 22:53 | comment | added | Asaf Karagila♦ | No, I am just curious as to the parameters of the question. Sometimes people think about this in very "bounded" terms, i.e. countably infinite. Or something like that. | |
| Nov 25, 2023 at 22:25 | history | closed |
Gerald Edgar Andrés E. Caicedo Steven Landsburg Aryeh Kontorovich Lee Mosher |
Not suitable for this site | |
| Nov 25, 2023 at 21:05 | review | Close votes | |||
| Nov 25, 2023 at 22:26 | |||||
| Nov 25, 2023 at 20:20 | comment | added | Michael Hardy | @AsafKaragila : Now I suspect that you want me to say more than any finite cardinality, so you can point out something wrong with that. | |
| Nov 25, 2023 at 20:11 | answer | added | Станислав Крымский | timeline score: 1 | |
| Nov 25, 2023 at 20:01 | answer | added | Noah Schweber | timeline score: 2 | |
| Nov 25, 2023 at 19:55 | comment | added | Asaf Karagila♦ | Define "infinitely many". | |
| Nov 25, 2023 at 19:48 | comment | added | Michael Hardy | @NoahSchweber : The bit about getting out of bed in the morning does have something to do with the actual math, if not with the question at the end. | |
| Nov 25, 2023 at 19:47 | comment | added | Michael Hardy | @NoahSchweber : ok, I've deleted part of this. | |
| Nov 25, 2023 at 19:46 | comment | added | Michael Hardy | @NoahSchweber : Perhaps . . . . but I thought some here might benefit from knowing of that book. I don't have it in front of me now and don't remember the specifics, but I should be able to dig it up. | |
| Nov 25, 2023 at 19:42 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 19 characters in body
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| Nov 25, 2023 at 19:41 | comment | added | Noah Schweber | I think there's an interesting question here, but a lot of the flavor text could be trimmed (I don't see what the first paragraph, or the bit about how long you personally took on the original version, or the bit about getting out of bed in the morning, have to do with the actual math here). And as usual with such common/shared-knowledge problems, the most obvious difficulty is even posing the problem precisely in the first place (which is why I think it's a good idea to avoid unnecessary flavor-text in this case). | |
| Nov 25, 2023 at 19:36 | history | asked | Michael Hardy | CC BY-SA 4.0 |