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The last sentence of the article reads:
" For example, the counterpart of 1 − 2 + 3 − 4 + ... in the zeta function is the non-alternating series 1 + 2 + 3 + 4 + ..., which has deep applications in modern physics but requires much stronger methods to sum."
But wait! If S = 1 + 2 + 3 + 4 + ... then
2S = 2 + 4 + 6 + 8+... and
-3S = S - 2(2S) = 1 + 2 + 3 + 4 + ... - 2(2 + 4 + 6 + 8+...) = 1 - 2 + 3 - 4 +....
So if the last summation has already been shown to have a nonstandard summation method assigning it a value of 1/4, then the sum S = 1 + 2 + 3 + 4 + ... can be readily assigned the value (-1/3)(1/4) = -1/12 without requiring "much stronger methods to sum". Daqu ( talk) 13:24, 22 October 2015 (UTC)
Does all of this equal 0 or something i don't get it Porygon-Z 23:16, 13 April 2019 (UTC) — Preceding unsigned comment added by Porygon-Z474 ( talk • contribs)
Does anybody know what resource exactly is cited here? Special:Diff/112109517. Nothing of Knopp's was added in the References section, and the reference just says "Knopp p.491" without a corresponding item in the Bibliography for 13 years now. (The original research phrasing "there appears" has been deleted in the meantime.) @ Melchoir: ping as the author, although I see you as inactive... Gikü ( talk) 20:45, 22 April 2020 (UTC)
I'm looking over this as part of the ongoing FA sweeps. There's a couple areas here that need some work here against the featured article criteria. Several places lack citations, the Weidlich source seems to fail WP:SCHOLARSHIP as it is only a masters thesis and does not seem to be widely cited, and there are tone issues, such as two places in the explanation of the formula where the reader is directly addressed as "we". This should be fixable if someone has the time and knowledge of the topic, although since big chunks of this article went straight over my head, that person is not me. Hog Farm Talk 21:37, 21 March 2021 (UTC)
Okay, so reading through this again most of this is probably self-proving. I'm not familiar with this subject, so there's a few areas that I'm not sure if it's obvious or not, so please be forgiving if I say anything stupid, because I really don't understand a lot of this subject.
I'll be removing this article from the noticed list, as I don't think the issues are anywhere close to a FAR, upon second reading. I think a copy edit would be nice here, as phrasings such as The last convergence sum is the reason illustrate why negative even values of Riemann zeta function are zero are a bit clunky, and someone familiar with math might want to check to make sure all the math markup is formatted in the preferred style, but this shouldn't be a giant project from this point. Hog Farm Talk 01:09, 11 June 2021 (UTC)
I think it's exactly the same argument as the talk with the title "Error?", though it stopped since 2007 so I've decided to make a new one.
In the Generalization Part of this article, the very first equation is the following:
Searching for the other equations related to this one, and found that the left side of the equation can be represented using the Dirichlet eta function. According to the definition, the left side becomes , and equation becomes the following:
Also, in the Dirichlet eta function article, on the Particular values section, there is a following equation:
Therefore, it seems like the equation should be the following, instead of the current one:
Cannot find the full citation for footnote Weidlich, pp. 52–55 in oldid 1180441176 while I was trying to improve the citation and references, after which I decided to put the work on hold. Dedhert.Jr ( talk) 01:13, 17 October 2023 (UTC)
This article is rated FA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
1 − 2 + 3 − 4 + ⋯ is a featured article; it (or a previous version of it) has been identified as one of the best articles produced by the Wikipedia community. Even so, if you can update or improve it, please do so. | |||||||||||||||||||
This article appeared on Wikipedia's Main Page as Today's featured article on April 15, 2007. | |||||||||||||||||||
|
|
|
This page has archives. Sections older than 730 days may be automatically archived by Lowercase sigmabot III when more than 5 sections are present. |
The last sentence of the article reads:
" For example, the counterpart of 1 − 2 + 3 − 4 + ... in the zeta function is the non-alternating series 1 + 2 + 3 + 4 + ..., which has deep applications in modern physics but requires much stronger methods to sum."
But wait! If S = 1 + 2 + 3 + 4 + ... then
2S = 2 + 4 + 6 + 8+... and
-3S = S - 2(2S) = 1 + 2 + 3 + 4 + ... - 2(2 + 4 + 6 + 8+...) = 1 - 2 + 3 - 4 +....
So if the last summation has already been shown to have a nonstandard summation method assigning it a value of 1/4, then the sum S = 1 + 2 + 3 + 4 + ... can be readily assigned the value (-1/3)(1/4) = -1/12 without requiring "much stronger methods to sum". Daqu ( talk) 13:24, 22 October 2015 (UTC)
Does all of this equal 0 or something i don't get it Porygon-Z 23:16, 13 April 2019 (UTC) — Preceding unsigned comment added by Porygon-Z474 ( talk • contribs)
Does anybody know what resource exactly is cited here? Special:Diff/112109517. Nothing of Knopp's was added in the References section, and the reference just says "Knopp p.491" without a corresponding item in the Bibliography for 13 years now. (The original research phrasing "there appears" has been deleted in the meantime.) @ Melchoir: ping as the author, although I see you as inactive... Gikü ( talk) 20:45, 22 April 2020 (UTC)
I'm looking over this as part of the ongoing FA sweeps. There's a couple areas here that need some work here against the featured article criteria. Several places lack citations, the Weidlich source seems to fail WP:SCHOLARSHIP as it is only a masters thesis and does not seem to be widely cited, and there are tone issues, such as two places in the explanation of the formula where the reader is directly addressed as "we". This should be fixable if someone has the time and knowledge of the topic, although since big chunks of this article went straight over my head, that person is not me. Hog Farm Talk 21:37, 21 March 2021 (UTC)
Okay, so reading through this again most of this is probably self-proving. I'm not familiar with this subject, so there's a few areas that I'm not sure if it's obvious or not, so please be forgiving if I say anything stupid, because I really don't understand a lot of this subject.
I'll be removing this article from the noticed list, as I don't think the issues are anywhere close to a FAR, upon second reading. I think a copy edit would be nice here, as phrasings such as The last convergence sum is the reason illustrate why negative even values of Riemann zeta function are zero are a bit clunky, and someone familiar with math might want to check to make sure all the math markup is formatted in the preferred style, but this shouldn't be a giant project from this point. Hog Farm Talk 01:09, 11 June 2021 (UTC)
I think it's exactly the same argument as the talk with the title "Error?", though it stopped since 2007 so I've decided to make a new one.
In the Generalization Part of this article, the very first equation is the following:
Searching for the other equations related to this one, and found that the left side of the equation can be represented using the Dirichlet eta function. According to the definition, the left side becomes , and equation becomes the following:
Also, in the Dirichlet eta function article, on the Particular values section, there is a following equation:
Therefore, it seems like the equation should be the following, instead of the current one:
Cannot find the full citation for footnote Weidlich, pp. 52–55 in oldid 1180441176 while I was trying to improve the citation and references, after which I decided to put the work on hold. Dedhert.Jr ( talk) 01:13, 17 October 2023 (UTC)