Timeline for On a strange step in the proof regarding a maximal problem.
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 15 at 1:27 | comment | added | fleablood | He's saying the average of groups of 15 is $15082.5$ there must be a consecutive group of 15 which is at least average. So there is a group of 15 that adds to $\ge 15082.5$. As any group of 15 must add to an integer there is a group of 15 that add to $\ge 15083$. That's why the ceiling function. But the more I think about it the more I feel it is not done. We can group them so that $a_1, ..., a_{15}$ and $a_16, ...., a_{30}$ etc all add to $18082$ and $18083$ but how do we show that that is true no matter where we break the grouping? | |
| Mar 15 at 1:19 | comment | added | fleablood | The thing I'm not seeing, is he doesn't seem to be giving any argument that he can arrange them so that none of the consecutive fifeteen add to more than 15083 even though he is clearly claiming that is the case. | |
| Mar 15 at 1:16 | comment | added | fleablood | He's not just showing that it is an example were there exist 15 sums at least equal to 15083. He is also showing that it is an example in which no fifteen consecutive are more than 15083. Since it's possible to arrange them so that no consecutive 15 are 15084 or more, the answer must be less than 15084. And since every way you arrange them you will always have 15 adding to at least 15083 the anwer must be at least 15083. So the answer must be at least 15083 but it must be less than 15084. That means it must be 15083. | |
| Mar 15 at 0:53 | comment | added | Henry | None of the groups can be exactly $15082.5$ as they are the sums of integers. If all $134$ were $15082$ or less then the overall sum would be $134\times 15082$ or less which is too small. So at least one group is $15083$ or more. | |
| Mar 15 at 0:48 | answer | added | Zumzumike | timeline score: 1 | |
| Mar 15 at 0:39 | comment | added | Robert Shore | The first part of the proof shows that the minimum must be at least $15083$. But that doesn’t prove the minimum is $15083$. It’s conceivable that some better proof might establish that the minimum has to be at least $15084$, or an even higher number. Providing an example shows that the potential minimum can in fact be achieved, so it really is the minimum, and not just a lower bound on the minimum. | |
| Mar 15 at 0:30 | history | asked | Ruben | CC BY-SA 4.0 |