Mathematics desk | ||
---|---|---|
< January 17 | << Dec | January | Feb >> | January 19 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
While waiting around for files in some large torrents to complete, I observed that, without specific files being assigned higher priority, the percentage of files complete is usually much lower than the percentage of the torrent complete, for obvious reasons (for example, if you have 30% of the entire torrent complete, it's likely that you have less than 5% of the files complete, because that 30%-completed is spread out between files, so that you have a little bit of many mostly incomplete files, and a very small number of fully-completed files where the pieces just happened to line up). I began to wonder exactly how many files you should expect to be complete, which got me to the following generalized question:
(Obviously, the above makes a few simplifying assumptions, as, in real life: not all files of a torrent will be equally-sized; users can configure clients to prioritize some pieces higher than others; pieces are downloaded based upon availability, which is not fully random; and pieces at the front- or tail-end of files will usually be shared between the files, containing bytes from both files.)
Anybody know how to solve the above problem? Do we have an article on this generalized problem, since I could see it applying to other situations besides torrents? (A similar problem: suppose a bucket is filled with 100 balls of 10 different colors, so that there is one ball of each color; after picking x balls without replacement, what is the expected number of colors for which you have every ball of that color?) Thanks.
— SeekingAnswers ( reply) 01:48, 18 January 2014 (UTC)
Can someone say something about this.. http://www.slate.com/blogs/bad_astronomy/2014/01/17/infinite_series_when_the_sum_of_all_positive_integers_is_a_small_negative.html [1] How can adding up infinite number of positive numbers get you a negative number? 220.239.51.150 ( talk) 03:40, 18 January 2014 (UTC)
The article in the url link specifically says that
220.239.51.150 ( talk) 12:28, 18 January 2014 (UTC)
This is clearly false, here is the proof. You will pay me one dollar on the first day, two dollars on the second day, three dollars on the third day and so on and so forth for ALL ETERNITY. But in reality, you don't owe me anything, instead I owe you eight cents and one third of a cent !!! Does that make any sense to you??? Ohanian ( talk) 07:15, 19 January 2014 (UTC)
So our article on Ramanujan summation, which is apparently what's used to assign a value to 1+2+3+..., strikes me as not the clearest math article I've ever seen on Wikipedia, but the idea filters through to me that one takes certain formulas for sums of the form Σf(n), where I'm being deliberately vague about the limits of summation, and then applies them outside the region where they can be proved to be correct in the sense of the ordinary absolutely convergent infinite sum, and then one declares that to be the answer. Yes?
If I've followed it that far, then to me, the obvious question is, do I get the same answer if I use a different function g, but one that agrees with f on the values that I'm summing? Maybe, if some regularity condition is imposed on g, say that it be an entire function or something? If so, then I can agree that this procedure is genuinely isolating a property of the sum itself. But if not, then it seems to be a property of a particular representation of the sum, and therefore not properly a sum of 1+2+3+... at all. Does anyone know? -- Trovatore ( talk) 00:42, 21 January 2014 (UTC)
Mathematics desk | ||
---|---|---|
< January 17 | << Dec | January | Feb >> | January 19 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
While waiting around for files in some large torrents to complete, I observed that, without specific files being assigned higher priority, the percentage of files complete is usually much lower than the percentage of the torrent complete, for obvious reasons (for example, if you have 30% of the entire torrent complete, it's likely that you have less than 5% of the files complete, because that 30%-completed is spread out between files, so that you have a little bit of many mostly incomplete files, and a very small number of fully-completed files where the pieces just happened to line up). I began to wonder exactly how many files you should expect to be complete, which got me to the following generalized question:
(Obviously, the above makes a few simplifying assumptions, as, in real life: not all files of a torrent will be equally-sized; users can configure clients to prioritize some pieces higher than others; pieces are downloaded based upon availability, which is not fully random; and pieces at the front- or tail-end of files will usually be shared between the files, containing bytes from both files.)
Anybody know how to solve the above problem? Do we have an article on this generalized problem, since I could see it applying to other situations besides torrents? (A similar problem: suppose a bucket is filled with 100 balls of 10 different colors, so that there is one ball of each color; after picking x balls without replacement, what is the expected number of colors for which you have every ball of that color?) Thanks.
— SeekingAnswers ( reply) 01:48, 18 January 2014 (UTC)
Can someone say something about this.. http://www.slate.com/blogs/bad_astronomy/2014/01/17/infinite_series_when_the_sum_of_all_positive_integers_is_a_small_negative.html [1] How can adding up infinite number of positive numbers get you a negative number? 220.239.51.150 ( talk) 03:40, 18 January 2014 (UTC)
The article in the url link specifically says that
220.239.51.150 ( talk) 12:28, 18 January 2014 (UTC)
This is clearly false, here is the proof. You will pay me one dollar on the first day, two dollars on the second day, three dollars on the third day and so on and so forth for ALL ETERNITY. But in reality, you don't owe me anything, instead I owe you eight cents and one third of a cent !!! Does that make any sense to you??? Ohanian ( talk) 07:15, 19 January 2014 (UTC)
So our article on Ramanujan summation, which is apparently what's used to assign a value to 1+2+3+..., strikes me as not the clearest math article I've ever seen on Wikipedia, but the idea filters through to me that one takes certain formulas for sums of the form Σf(n), where I'm being deliberately vague about the limits of summation, and then applies them outside the region where they can be proved to be correct in the sense of the ordinary absolutely convergent infinite sum, and then one declares that to be the answer. Yes?
If I've followed it that far, then to me, the obvious question is, do I get the same answer if I use a different function g, but one that agrees with f on the values that I'm summing? Maybe, if some regularity condition is imposed on g, say that it be an entire function or something? If so, then I can agree that this procedure is genuinely isolating a property of the sum itself. But if not, then it seems to be a property of a particular representation of the sum, and therefore not properly a sum of 1+2+3+... at all. Does anyone know? -- Trovatore ( talk) 00:42, 21 January 2014 (UTC)