Wikipedia talk:WikiProject Mathematics

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Emmy Noether FAR final citations and checks

The Emmy Noether article has been at featured article review for a couple months now. If anyone wants to take a look, most of the issues seem to have been fixed but the contributions to mathematics and physics section would likely benefit from a couple more citations and a quick survey (including of the typsetting) by someone more qualified than I am. Sgubaldo (talk) 15:20, 16 April 2024 (UTC)

In particular, does anyone feel like tackling the subsection Emmy Noether#Ascending and descending chain conditions? XOR'easter (talk) 17:00, 1 May 2024 (UTC)

Adjoint functor theorem

I think that people searching for "Adjoint functor theorem" are looking for explanations about the Freyd's adjoint functor theorem, so I suggest changing the redirect target to the Formal criteria for adjoint functors. SilverMatsu (talk) 15:35, 24 April 2024 (UTC)

Ths is a possibility. However, there is an anchor "Freyd's adjoint functor theorem" in Adjoint functors. I have changed the redirect for pointing to this anchor instead of to the lead. Note that Formal criteria for adjoint functors is linked to just above this anchor. I have no clear opinion about your proposed change of target, but, in any case, Freyd's adjoint functor theorem and Adjoint functor theorem must have the same target. D.Lazard (talk) 16:24, 24 April 2024 (UTC)

Thank you for clarifying the redirect target. By the way, there are two versions of Freyd's adjoint functor theorem, which are sometimes called General adjoint functor theorem and Special adjoint functor theorem. --SilverMatsu (talk) 00:19, 25 April 2024 (UTC)

Requested move at Talk:Basic Math (video game)#Requested move 24 April 2024

There is a requested move discussion at Talk:Basic Math (video game)#Requested move 24 April 2024 that may be of interest to members of this WikiProject. RodRabelo7 (talk) 05:33, 28 April 2024 (UTC)

"Distinct" definition

The use of the word "distinct" , should be reviewed , so that its usage becomes clear, here are the pages I have noticed them in: Constructible polygon, ,Carl Friedrich Gauss ,Exact trigonometric values ,Constructible number

The constructible polygon page says : A regular n-gon can be constructed with compass and straightedge if and only if n is a power of 2 or the product of a power of 2 and any number of distinct Fermat primes.

Whereas , the Constructible number page says:

• powers of two
• Fermat primes, prime numbers that are one plus a power of two
• products of powers of two and any number of distinct Fermat primes.

Notice here the second bullet point is separate to the third ; is that to say that "any number of distinct Fermat primes" does not include one Fermat prime appearing on its own. And would zero Fermat primes be considered a distinct number of Fermat primes?. This should be specified. EuclidIncarnated (talk) 13:48, 28 April 2024 (UTC)

The formatting of the post above is difficult to read. As far as I can tell, the issue is more about "any number" than about "distinct". I think that it is best treated by editing those specific pages to address that specific issue. Mgnbar (talk) 14:03, 28 April 2024 (UTC)

Sorry about my bad formatting , I am relatively new to Wikipedia writing and thank you for bringing to my attention , "any number", which should be defined more clearly. I would say that so does "distinct". For example , consider one number is it distinct? or is there required a second number for it to be said to be distinct?. Such things should be made more clear. EuclidIncarnated (talk) 14:44, 28 April 2024 (UTC)

As an example, I have edited Constructible polygon#Conditions for constructibility. I did not clarify what "distinct" means, but I did clarify (some might say too explicitly) what "any number" means. What do you think of this solution? Does "distinct" still require clarification? Mgnbar (talk) 15:03, 28 April 2024 (UTC)

I changed the ·bullets to asterisks to make a proper list. —Tamfang (talk) 19:38, 28 April 2024 (UTC)

The last bullet point includes the first two bullet points as special cases. –jacobolus (t) 14:22, 28 April 2024 (UTC)

I don't see how the first bullet point is a special case of the last bullet point , could you explain what you mean? EuclidIncarnated (talk) 15:03, 28 April 2024 (UTC)

In the third bullet point, let 2^j be the power of 2 involved, and let k be the number of distinct Fermat primes involved. The first bullet point is the special case where k = 0. The second bullet point is the special case where k = 1 and j = 0. Mgnbar (talk) 15:44, 28 April 2024 (UTC)

Yes this is going off of the definition that the product of a number is itself and thus a power of 2's product is itself. This is what Product (mathematics) says is the definition of products : "Originally, a product was and is still the result of the multiplication of two or more numbers." Therefore your definition of product is not this. EuclidIncarnated (talk) 17:47, 28 April 2024 (UTC)

Sorry; I don't quite understand your post. No one here has defined the word "product", have they? The Wikipedia article Product (mathematics) is not a Wikipedia:Reliable source. Anyway, products and powers can take on slightly different meanings in different contexts. When stating a theorem, it is a good idea to make the intended meaning explicit and clear.

Have you seen my recent edit to Constructible polygon#Conditions for constructibility, which I mentioned above? Is it not clear? Regards, Mgnbar (talk) 18:01, 28 April 2024 (UTC)

It seems fine to me , your edit. EuclidIncarnated (talk) 18:11, 28 April 2024 (UTC)

@EuclidIncarnated Mathematicians define the "product" of any (possibly empty) collection of elements all belonging to some structure where multiplication is well-defined. An empty product is equal to the multiplicative identity, which is 1 in the case the quantities being multiplied are numbers. The "product" of a single quantity is just the quantity itself. –jacobolus (t) 00:09, 29 April 2024 (UTC)

All true, but this is a point we should be careful of when writing articles for non-mathematicians who may become confused by 0-element and 1-element products. —David Eppstein (talk) 00:29, 29 April 2024 (UTC)

Is there anywhere in Wikipedia that has such a definition. EuclidIncarnated (talk) 07:12, 29 April 2024 (UTC)

@EuclidIncarnated This is described in Product (mathematics) § Product of a sequence. While a sequence per se is an ordered list of numbers (or other quantities), if multiplication is commutative (true in many but not all contexts) the order doesn't matter and you could just as well take the product of an unordered collection like a multiset. –jacobolus (t) 07:15, 29 April 2024 (UTC)

And Product (mathematics)#Empty product is all about the case where 0 numbers are being multiplied. Mgnbar (talk) 11:59, 29 April 2024 (UTC)

Wigner probability distribution

It might be good to have some people watch Wigner semicircle distribution, with someone having just added back some extensive material I deleted a couple months ago. I think it's pretty incoherent, and not good material for the page regardless. Gumshoe2 (talk) 16:22, 28 April 2024 (UTC)

Log vs ln

On Talk:Ordered Bell number, an editor is arguing that we should use ln rather than log for the natural logarithm. My position is that for mathematics articles, the standard convention is to use log; ln is for engineers and this is not an engineering article. The same editor also claims that writing $\log _{2}e$ is "stupid" and that we should always write it ${\tfrac {1}{\ln 2}}$ instead. Mathematically-literate opinions welcome. (Note that the article is currently in the middle of a GA review; the editor disputing the notation is not the GA reviewer.) —David Eppstein (talk) 18:30, 1 May 2024 (UTC)

Maybe we can add this to a style guide somewhere. I think it's worth using ln in articles about engineering and possibly also in high-school-level topics such as those related to trigonometry or introductory calculus. I'd rather use log everywhere else, wherever it isn't ambiguous. –jacobolus (t) 18:35, 1 May 2024 (UTC)

I prefer $\ln x$, but as long as the article clearly sets out the nomenclature that it's using, it's no big deal.

WRT "${\tfrac {1}{\ln 2}}$", eschew obfuscation; it's confusing and ugly. I see nothing wrong with $\log _{2}e$ -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 21:20, 1 May 2024 (UTC)

How about Logarithmic integral function? You wouldn't write $\int _{0}^{x}\log _{t}e\ \mathrm {d} t$. IntGrah (talk) 22:22, 1 May 2024 (UTC)

Whether to write 1/log_e2 depends on the context. For starters, what if you're informing students of the basic facts about logarithms, which they just heard of today? Then you might state, as an example, that 1/log_e2 = log₂e, and then you'd need to write 1/log_e2. Michael Hardy (talk) 21:10, 2 May 2024 (UTC)

Presumably someone reading Ordered Bell number isn't learning about logarithms for the first time. –jacobolus (t) 21:55, 2 May 2024 (UTC)

• "My position is that for mathematics articles, the standard convention is to use log;"

All you need is a reference to cite this standard convention. Johnjbarton (talk) 22:32, 1 May 2024 (UTC)

You don't need a reference for this. This is prevailing practice throughout the mathematics literature. (It's not hard to find such references, but throwing them in is off-topic for whatever article, and gratuitous.) However, it could help to briefly note, in contexts where some readers might be confused, that log means the natural logarithm, with a wikilink. –jacobolus (t) 22:35, 1 May 2024 (UTC)

In the early days of Wikipedia, user:AxelBoldt was the author of a majority of mathematics articles on Wikipedia, and argued that ln is better than log because it is unambiguous.

I prefer log or log_e. Notice that exp does not mean base-10 exponential.

Undergraduates not majoring in mathematics sometimes say "Do you mean logarithm, or natural logarithm?" (to which the correct answer is usually "yes."). The use of ln has misled them to think that the natural logarithm is not literally a logarithm. (They have also often been taught to call the inverse tangent function the inverse tangent function and have never encountered the word "arctan". If you write "arctan θ" then one of them asks whether "arctangent" is the same as "cotangent.") Michael Hardy (talk) 20:56, 2 May 2024 (UTC)

If using $\,\arctan \theta \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{\color {RawSienna}{\tfrac {\qquad \quad \ \ }{}}}\ \theta =\arctan x$ in some arbitrary article, it can be helpful to add an inline definition, along the lines of "where $\arctan$ is the trigonometric inverse tangent function". –jacobolus (t) 21:55, 2 May 2024 (UTC)

If I came across $\arctan \theta$ I'd worry I'd done something wrong! NadVolum (talk) 14:11, 3 May 2024 (UTC)

I think that $\ln x$ makes it clear that anti-logarithm x is a real number rather than making it clear that the base is e. In particular, clarify that the domain of a function of the $\ln x$ is real numbers. see principal value. --SilverMatsu (talk) 04:45, 3 May 2024 (UTC)

I was going to say I didn't mind what was used but I agree, yes you're right. lt does make it clear one is working with real numbers. NadVolum (talk) 14:11, 3 May 2024 (UTC)

Is there any Wikipedia article on which this technicality is worth bringing to the attention of the readers?

(FWIW despite being about combinatorics the context for the log in the article initiating this discussion actually does involve complex numbers.) —David Eppstein (talk) 18:04, 3 May 2024 (UTC)

This is not a universal convention, so I don't think it is a good idea to pretend it is. —Kusma (talk) 19:26, 3 May 2024 (UTC)

+1 to Kusma. When I see $\ln$ I do not necessarily automatically assume that the domain is the reals. I've seen that convention so it wouldn't especially surprise me to find someone using $\ln$ and $\log$ distinctively in that way, but I don't think it makes the domain unambiguous without further comment. --Trovatore (talk) 19:48, 3 May 2024 (UTC)

In Logarithm#Complex logarithm the convention is used with good effect in the definition of the complex logarithm. NadVolum (talk) 17:25, 6 May 2024 (UTC)

I find the use there to be confusing, inconsistent, and idiosyncratic. YMMV. I would much prefer if the multi-functions for argument and logarithm were capitalized, with names for the principal branch left all lowercase, matching the names of single-valued functions used elsewhere in the article and the more typical convention found in the literature (though this is a place where literature is notoriously inconsistent and confusing). –jacobolus (t) 19:00, 6 May 2024 (UTC)

By the way there is a standard to use lb for the binary logarithm but I don't know of anyone who does that! And using a base with ln is just silly. Only a total massochist would try using any base other than e with a complex logarithm so there's no point in specifying it in that case. NadVolum (talk) 17:39, 6 May 2024 (UTC)

I have often seen lg for the binary log. —Tamfang (talk) 01:12, 7 May 2024 (UTC)

Yes, that's pretty common, and approved by the Chicago Manual of Style, despite ISO explicitly reserving lg for common logarithms instead. (I have never seen any actual use of lg for common logs outside of ISO documents.) It's also pretty common for computer scientists (and sometimes information theorists) to use log for binary logarithms (without any base subscript), unfortunately, with hard-to-spot disclaimers that they're doing so. —David Eppstein (talk) 07:00, 7 May 2024 (UTC)

Knuth uses "lg" for the binary logarithm, and people probably pay more attention to Knuth than to the ISO. XOR'easter (talk) 16:16, 7 May 2024 (UTC)

FWIW I've seen several computer science papers using log for the base 2 logarithm, a single one using lb, and non using lg. Tercer (talk) 20:24, 7 May 2024 (UTC)

I can find several of my papers using lg. Nowadays I might be more likely to use log₂. But in much of computer science the logs are wrapped in O-notation and it doesn't matter what the base is; I think in that context log is the most likely notation. —David Eppstein (talk) 20:45, 7 May 2024 (UTC)

Merger of Unitary operator and Unitary transformation.

We have these two articles: Unitary operator, Unitary transformation. Should they get merged? Michael Hardy (talk) 21:04, 2 May 2024 (UTC)

I always thought the map C² → C³ given by sending (u, v) to (u, v, 0) would be an example of a unitary operator, with 'unitary' referring just to the preservation of a hermitian inner product. The notion suggested here is what I would call "unitary isomorphism." Have I been using the term in an unusual way? Gumshoe2 (talk) 18:59, 3 May 2024 (UTC)

Frobenius theorem

Could someone take a look at my suggestion here? Alaexis_¿question? 13:08, 6 May 2024 (UTC)