Talk:Summation

Content dispute

@172.77.243.224: Can you please explain why you removed a bunch of information? @Citizen Canine: and @Gdog1102:, what do you think about this? INeedSupport^{(Care free to give me support?)} 01:34, 25 October 2018 (UTC)

Nevermind. It would appear that the IP was vandalizing the article INeedSupport^{(Care free to give me support?)} 02:08, 25 October 2018 (UTC)

184.13.109.29 (talk) 18:05, 25 October 2018 (UTC) D Lazard edited the page again. Here is how I can tell: The banner at the top of the page https://en.wikipedia.org/wiki/Summation reads "This article may require cleanup to meet Wikipedia's quality standards." When I edit the page, the banner goes away. I tried editing the summation page to fit the wiki encyclopedia style. I also revised the grammar, spelling, and references for correctness and clarity. D Lazard likes his(her) version. The first sentence has a personal pronoun referring to a sum. Keep reading each sentence...more errors follow. 184.13.109.29 (talk) 18:05, 25 October 2018 (UTC)

184.13.109.29 (talk) 18:54, 25 October 2018 (UTC) Here are some more edits: 1) The "Formal Definitions" section does not define recursion. 2) The last formula in the section titled "Summation index in exponents" is a partial proof. Remove the derivation. 3) The section titled "Growth rates" is irrelevant to this page. Delete the entire section and add it to a different wiki page. 4) The section titled "Miscellaneous" has an existing wiki page on harmonic numbers. Delete this section and add it to the wiki page on harmonic numbers. 5) The links for the citation to Graham et. al. either do not work or are irrelevant to the citation. Remove the links.

Most likely, there are other errors on this page. 184.13.109.29 (talk) 18:54, 25 October 2018 (UTC)

I'll look at the information to see if you're correct, should I have time to do that. INeedSupport^{(Care free to give me support?)} 23:15, 25 October 2018 (UTC)

@184.13.109.29: Update: Looks like RLGoodwin is doing the work there. INeedSupport^{(Care free to give me support?)} 23:17, 25 October 2018 (UTC)

Incorrect General Identities

I KEEP removing these identities and someone keeps putting them right back in without checking correctness. Distributivity and factorization on the list are INVALID. If it doesnt work for a binomial why would anyone assume it worked for an arbitrary series? Hate fighting idiots on wikipedia. If you are weak at math and dont know what youre talking about, and wont even research, then quit contributing. Simple. Im starting to think its malice rather than stupidity. 50.125.86.70 (talk) 18:41, 25 February 2019 (UTC)

Which identities are wrong and what are the correct identities? Note that in the comments, "distributivity", ... do not mean that the identity makes the property explicit, but rather that this is used for proving the identity. D.Lazard (talk) 19:20, 25 February 2019 (UTC)

Change "natural numbers" to "positive integers" in lede

The lede currently says

For example, summation of the first 100 natural numbers may be written as 1 + 2 + 3 + 4 + ⋯ + 99 + 100. Otherwise, summation is denoted by using Σ notation, where ${\textstyle \sum }$ is an enlarged capital Greek letter sigma. For example, the sum of the first n natural numbers can be denoted as ${\textstyle \sum _{i=1}^{n}i.}$

"Natural numbers" should be changed to "positive integers". Two reasons for this:

1. Many definitions, including the official standard ISO 80000-2, include 0 in the natural numbers. "Natural numbers" may or may not include 0, while "positive integers" always excludes 0. A more precise term is preferable to a less precise one. Why use an ambiguous term when an unambiguous one exists?

2. The rest of the article (see the section titled "Powers and logarithm of arithmetic progressions") also uses the convention of including 0 in the natural numbers.

User D.Lazard has insisted on reverting this constructive edit, without providing a justification. Their actions suggest WP:OWNBEHAVIOR. 2001:569:7F68:BF00:1967:F693:74B7:F460 (talk) 21:39, 3 November 2021 (UTC)

There no WP:OWNBEHAVIOR here, as your change has been reverted by two different editors, none of which being the author of the disputed sentence. On the other hand there is a clear problem of WP:Edit warring, since you tried 4 times to make the same change.

ISO is not and has never been a standard for mathematics. It is not an official standard, as ISO is a private company. However, ISO is commonly used as a standard in engineering. This article is not about engeenering, so the reference to ISO is irrelevant.

MOS:MATH#Article introduction says "The lead should, as much as possible, be accessible to a general reader, so specialized terminology [...] should be avoided". Here "positive integer" is a (mathematical) specialized terminology, as "positive" and "integer" are taught to kids a long time after they know natural numbers.

The sentence, as it is currently, is absolutely not ambiguous, as I do not know anybody who understand "the 100 first natural numbers" as not containing 100. Moreover, in the case of a doubt, this is clarified by the formula that follows. So, the unneeded use of a technical terminology that you suggest is a form of pedantry.

Your reference to the rest of the article is a fallacy, as "positive integer" is used once in a formula where excluding zero is fundamental, while "natural number" is used three time, without indicating whether zero is included, except for the third formula that remains true if the term of index 0 is ommitted. D.Lazard (talk) 10:02, 4 November 2021 (UTC)

Response:

It is not an official standard, as ISO is a private company.

ISO is an independent, non-governmental international organization with a membership of 166 national standards bodies.

However, ISO is commonly used as a standard in engineering. This article is not about engeenering, so the reference to ISO is irrelevant.

It is also used as a standard in chemistry, physics, and mathematics. See ISO 31-11 for an example.

MOS:MATH#Article introduction says "The lead should, as much as possible, be accessible to a general reader, so specialized terminology [...] should be avoided". Here "positive integer" is a (mathematical) specialized terminology, as "positive" and "integer" are taught to kids a long time after they know natural numbers.

1. The term "integer" is not "specialized terminology". "General reader" does not mean "preschooler".

2. The term "natural number" (as opposed to simply "number") is no less "technical" than "integer".

3. I linked it to the article on integers.

The sentence, as it is currently, is absolutely not ambiguous

It absolutely is ambiguous, since "natural numbers" may or may not include 0.

"positive integer" is used once in a formula where excluding zero is fundamental

Irrelevant.

"natural number" is used three time, without indicating whether zero is included

The two formulas I'm referring to do include 0. Underneath the summation symbol is $i=0$, meaning the summation starts at 0.

except for the third formula that remains true if the term of index 0 is ommitted

Irrelevant. It is not true in the general case that $\sum _{i=0}^{n}a_{i}=\sum _{i=1}^{n}a_{i}$. 2001:569:7F68:BF00:34:F758:DCF1:F531 (talk) 21:33, 4 November 2021 (UTC)

How about replacing "summation of the first 100 natural numbers" with "summation of natural numbers from 1 to 100"? However, in the sentence immediately after it, it says "1 + 2 + 3 + ... + 100", so I think it's clear even as it is now.--SilverMatsu (talk) 22:42, 4 November 2021 (UTC)

Relationship between summation and repeated multiplication

Defining a relationship between these two will be good. Yuthfghds (talk) 17:23, 10 July 2023 (UTC)

Which relationship have in mind? For the relationship between repeated addition and multiplication, see the second paragraph of Multiplication and Multiplication and repeated addition. D.Lazard (talk) 19:39, 10 July 2023 (UTC)

"Finite series" should be mentioned somewhere

As discussed in the series talk page, the term "finite series" should be mentioned somewhere. (And don't say it's not a thing.) 2600:1012:A021:7A65:AD81:13C9:15D2:E5DF (talk) 04:01, 17 May 2025 (UTC)

The term was mentioned in the article. I have just bolded it and created the redirect Finite series. D.Lazard (talk) 08:39, 17 May 2025 (UTC)

Yes, the term is mentioned now because... I just added it. 2600:1012:A021:7A65:AD81:13C9:15D2:E5DF (talk) 14:35, 17 May 2025 (UTC)