Timeline for How many subsets I of $\{1,\cdots,n\}$ exist?
Current License: CC BY-SA 3.0
15 events
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| Jul 16, 2016 at 16:25 | vote | accept | CommunityBot | ||
| Jul 16, 2016 at 15:27 | comment | added | Fedor Petrov | Though the question is not well formulated, it is, after all, quite reasonable. | |
| Jul 16, 2016 at 15:25 | history | edited | user6671 | CC BY-SA 3.0 |
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| Jul 16, 2016 at 15:16 | answer | added | Fedor Petrov | timeline score: 9 | |
| Jul 16, 2016 at 15:15 | history | edited | user6671 | CC BY-SA 3.0 |
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| Jul 16, 2016 at 15:01 | history | edited | user6671 | CC BY-SA 3.0 |
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| Jul 16, 2016 at 15:00 | comment | added | Fedor Petrov | but I think that $a_2=0$ | |
| Jul 16, 2016 at 14:56 | comment | added | user6671 | I edited the question to show the computation of $n=3$. | |
| Jul 16, 2016 at 14:55 | history | edited | user6671 | CC BY-SA 3.0 |
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| Jul 16, 2016 at 14:49 | comment | added | Willie Wong | My previous comment lists $b_n$ if they are proper subsets. If they are not then you add 2. They don't seem to agree with your $a_n$. (In particular, how is $a_2 = 2$ when $a_1 = 0$? If you count only proper subsets, $b_1 = 0$ and $b_2 = 2$. But if you count all subsets, $b_1 = 2$ and $b_2 = 4$.) Can you do a few examples to show how you computed "manually" those numbers? | |
| Jul 16, 2016 at 14:42 | history | edited | user6671 | CC BY-SA 3.0 |
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| Jul 16, 2016 at 14:42 | comment | added | Willie Wong | Do you require proper subsets? Also, your sequence seems wrong. For $n = 3$ you have $\{1\}, \{2\}, \{1,3\}, \{2,3\}$. For $n = 4$ I get at least 10: $\{1\}, \{2\}, \{3\}, \{1,2\}, \{1,3\}$ and their complements. For $n = 5$ you should have $$ \{1\}, \{2\}, \{3\}, \{4\}, \{1,2\}, \{1,3\}, \{1,4\}, \{2,3\}, \{2,4\} $$ and their complements. So it seems you inserted an extra $2$ in your sequence? | |
| Jul 16, 2016 at 14:18 | comment | added | user6671 | Yes, thats what I mean. | |
| Jul 16, 2016 at 14:17 | comment | added | Fedor Petrov | You mean that this inequality holds for all sequences $0<x_1<\dots <x_n$? | |
| Jul 16, 2016 at 13:51 | history | asked | user6671 | CC BY-SA 3.0 |