Talk:Exponentiation/Archive 2020

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Commutative exponentiation (?)

Could an expert page-watcher please review Commutative exponentiation, and (if appropriate) link it into Exponentiation#Identities_and_properties and Hyperoperation#Commutative_hyperoperations. Thanks ^~Hydronium^~Hydroxide^~(Talk)~ 03:28, 4 March 2020 (UTC)

I have redirected this article to Hyperoperation#Commutative hyperoperationsHyperoperation#Commutative hyperoperations, a Google scholar . D.Lazard (talk) 10:38, 4 March 2020 (UTC)

Although the concept is described (but with a different name) in Hyperoperation#Commutative hyperoperations, a Google Scholar search reveals that "commutative exponentiation" commonly refers to another concept, although this phrase is rarely used. Therefore, I have added here a section Exponentiation#Powers of a sum, and redirect the article there. D.Lazard (talk) 16:43, 4 March 2020 (UTC)

First power never mentioned

It feels like an oversight to have this entire treatise on exponents without a single mention of raising to the power of one. — Preceding unsigned comment added by Freswinn (talk • contribs) 05:55, 18 March 2020 (UTC)

Good point. The power of one appears is section "Positive exponents". Nevertheless, this should be in the lead, and I have added it. D.Lazard (talk) 10:54, 18 March 2020 (UTC)

Reviving archived question: "Graph of y = b^x for base 10"

This was asked by @002Frank: but it was archived before anyone replied, so I'm reviving and answering:
I am not an expert, but I am confused by the first graph depicted which includes was supposed to be a graph of y = b^x for base 10. Shouldn't that graph look like the following:

graph of the function y = b^x with b from -3 to 3

The photo in the article shows different exponential functions with different bases b, but the independent variable is x. Your graph has b as the independent variable, so you have a power function, not an exponential. Cpotisch (talk) 20:00, 29 December 2020 (UTC)

GA Reassessment

This discussion is transcluded from Talk:Exponentiation/GA1. The edit link for this section can be used to add comments to the reassessment.

I am going to be reassessing this article in line with the good article criteria. If there is any interest from people to save this article, I will provide more detailed feedback. Issues that I see immediately are:

• Extremely significant portions of unsourced text throughout, including unquestionably valid citation needed and better source needed tags, and entire sections that are unsourced. (eg: Terminology)
• Subsection without any content (Powers of three)
• Sandwiching concerns under Power functions (not a GA requirement AFAIK but still should be addressed)
• Subsection without any point or explanation (List of whole-number powers)
• Unquestionably valid textbook tag
• Meaningless (?) statements like This is the starting point of the mathematical theory of semigroups - which may not be wrong but don't mean anything, and are better suited for a textbook
• A quandle is an algebraic structure in which these laws of conjugation play a central role - vagueness concerns
• A field is an algebraic structure in which multiplication, addition, subtraction, and division are all well-defined and satisfy their familiar properties - vagueness concerns
• Elaboration needed in "In category theory"
• Entirely malformed citation 40 - and NPOV concerns ("points out" - see MOS:SAID)
• Not a GA requirement so always free to ignore, but citation style consistency is probably useful
• Entire books like Hille and Phillips' Functional Analysis and Semi-Groups are being cited which poses WP:V concerns

I will notify some interested parties and projects to hopefully keep the GA status, but it will unquestionably be a lot of work, so I understand if nobody has the appetite. Even if it's not saved, hopefully we can get it in better condition. Thanks, Urve (talk) 09:28, 5 August 2021 (UTC)

Also

• Remove from footnotes extensive discussions on notations that are used by a single (WP:OR) or very few (WP:Notability) authors. D.Lazard (talk) 09:57, 6 August 2021 (UTC)

Finite fields and modular exponentiation

I have rewritten the section "Finite fields" for focusing on exponentiation and providing the important specific properties of this case.

By the way, Modular exponentiation appears only in section "See also". IMO, it deserve a specific section, with links to Fermat's little theorem and Euler's theorem and mentions to main applications such as RSA (cryptosystem) and polynomial factorization.

Also, the place of these sections in the article deserve a discussion. D.Lazard (talk) 10:11, 6 August 2021 (UTC)

Some great work. Thank you! Urve (talk) 07:06, 14 August 2021 (UTC)

Remaining issues

@Urve: What are the remaining points to be addressed? D.Lazard has revised much of the article to good effect since the list was initially posted here, so it would be helpful to know what's left :) — MarkH₂₁^talk 08:21, 16 September 2021 (UTC)

My main concern is the extensiveness of uncited text, which includes entire subsections. Some of these are okay because they're not reasonably expected to be challenged, but others are especially problematic in discussing specific results, terminological usage, or main theorems and their consequences, because they can't be verified. I'm on vacation for a few more days but will take a closer look soon. Urve (talk) 10:28, 16 September 2021 (UTC)

I am still not happly with some sections, specially the last three subsections of § Integer powers in algebra and the section § Limits of powers, which deserve to be completely rewritten. Also there is a lacking section on "powers under exponentiation", in which, among other things, it must be said that iterative methods (for example Newton's method) consist generally of finding a fixed point of a function as the limit of the powers under function composition of another function. D.Lazard (talk) 10:30, 16 September 2021 (UTC)

I see that you've been working on this, D.Lazard, and I appreciate your effort a lot - the prose has elevated and what you've worked on has improved. Do you still have the appetite to continue, or should we close this out? Again, some things are OK, but my main concern is how extensive uncited text is. I would fix most of this up myself, but my impression is that many of the results here are contained in textbooks or in unreliable web sources, so I can't be of much help. Just let me know what you're thinking... I'm OK with having this open for as long as needed, but if you don't want to continue, I can't blame you. Urve (talk) 22:54, 15 October 2021 (UTC)

• @Urve, MarkH21, and D.Lazard: Are we making progress here? It has been open a while now. Aircorn (talk) 04:34, 13 November 2021 (UTC)
  • I don't think so. I wanted to give about a month since my ping above (October 15) to determine whether there was any interest in working on the article, whether by drive by editors or people here, before closing out the GAR. Urve (talk) 06:30, 13 November 2021 (UTC)
  • As said above, I am not happy with the mathematical content of two sections. Nevertheless, I'll not edit them in a near future because I am presently engaged in editing Mathematics, which is a level-1 vital article, and is in a much worst state than this level-3 vital article. D.Lazard (talk) 09:38, 13 November 2021 (UTC)