User talk:Rgdboer

To facilitate current discussion an archive has been established to clear this page for 2017.Rgdboer (talk) 02:40, 22 December 2016 (UTC)

Undoing edits

Hey, there!

I see that you undid all of my edits from last night on Protein combining without entering any information as to why. Please refrain from doing that. Let me know if you have any questions.

Thanks!

--SaletteAndrews (talk) 20:47, 13 January 2017 (UTC)

The article is very controversial, with dietitians versus biochemists. My contributions to the article ceased in January 2017. However, recently two sources for Liebig's law of the minimum#Protein nutrition have been provided, and these support the biochemists. Rgdboer (talk) 03:04, 5 September 2022 (UTC)

Laurence Clancy

Hello Rgdboer. I was delighted to see you started a new article on Laurence Joseph Clancy! I started an article on the same person in about 2008 but after a few months it was listed for deletion and, despite my best efforts, the listing was successful. You can read the deletion debate at Wikipedia:Articles for deletion/Laurence Clancy. This will show the sort of argument people brought to bear to have "my article" deleted in 2008, and the sort of argument we need to be able to combat in 2017.

You may wish to ask an Admin to retrieve my 2008 article in order to see what it said, and what citations were supplied. Either way, I am happy to contribute to your new article to make it as robust as possible so it can withstand any future deletion debate.

I continue to cite Clancy in most of the aerodynamics articles I work on, so I am very glad Wikipedia again has some information about him. Best wishes, Dolphin (t) 03:42, 16 January 2017 (UTC)

PS: I have asked an Admin to send me the text of my 2008 article; see my diff. Let me know if you want a copy. Dolphin (t) 02:41, 18 January 2017 (UTC)

PPS: User:RHaworth has restored the 2008 edits to the history of Laurence Joseph Clancy. Earlier versions can be seen by selecting them in the history of the current article. Dolphin (t) 04:04, 19 January 2017 (UTC)

I was going to be eliminating those subheader titles that you changed, but thanks!

The way that the section in Spacetime was going, I was going to delete the subheaders, but thanks! I've always appreciated your contributions! Stigmatella aurantiaca (talk) 23:13, 24 March 2017 (UTC)

Liebmann (1905)

You wrote in Möbius_transformation#Lorentz_transformation, that Liebmann (1905) noted the isomorphism between Lorentz group and Möbius group. However, the 1905 edition of his "Nichteuklidische Geometrie" does not contain (as far as I can see) any discussion of the Lorentz group (in the 1923 edition there is a little bit). I think a better source is Herglotz (1909), who pointed out that "Lorentz transformations definitely correspond to hyperbolic motions in $R_{3}$", transforming the unit sphere into itself (p. 407). Using Klein's classification of hyperbolic motions, Herglotz separated the one-parameter Lorentz transformations into loxodromic group, hyperbolic group, elliptic group, and parabolic group (p. 408). --D.H (talk) 11:30, 28 June 2017 (UTC)

Thank you for the notes and links on this fascinating topic. Given that special relativity is a branch of linear algebra (with physical content), the alignment of the Riemann sphere with the celestial sphere accomplishes the Möbius-Lorentz group correspondence. Liebmann was cited because Coxeter mentioned him, but now it seems Herglotz is more appropriate. These century-old sources show that Penrose was a late-comer to this topic. — Rgdboer (talk) 23:22, 28 June 2017 (UTC)

I've now included a description of the formulas of Fricke & Klein (1897) and Herglotz (1909) in Spherical_wave_transformation#Conformal_group_isomorphic_to_Lorentz_group. Regarding Liebmann (1905), on pp. 52ff. he discussed the relation between hyperbolic motions and "Kreisverwandtschaften" (Möbius transformations), obtaining and extending some results of Fricke & Klein (without citing them). In the third edition of his book from 1923 (on p. 143), Liebmann mentioned the relationship between Lorentz transformations and motions of the hyperbolic plane using Weierstrass coordinates. --D.H (talk) 11:59, 20 July 2017 (UTC)

The following relevant reference has flaws:

• Remi Langevin (2015) Integral Geometry from Buffon to Geometers of Today, chapter 18 "Integral geometry of Lorentz spaces", page 147, Société mathématique de France ISBN 978-2-85629-822-0

The misprint in the description of P_z (third line from bottom of page) has ${\mathcal {L}}(x,z)=1$ where it should be ${\mathcal {L}}(x,z)=0.$ This orthogonality property is given at the outset, but omits to mention hyperbolic orthogonality as the non-perpendicular meaning in this case. The use of Möbius name is overly broad, being invoked for SO(1,1) and the term Mob used instead of Lorentz group as is standard. Langevin's effort to sketch the Mobius-Lorentz group isomorphism is a gloss, not a proof. Rgdboer (talk) 01:37, 25 December 2017 (UTC) — Rgdboer (talk) 01:46, 25 December 2017 (UTC)

You may be interested in

• Homersham Cox (mathematician)#Work on non-Euclidean geometry or
• Gustav von Escherich#Work on hyperbolic geometry,

as well as in the recent additions to

• History of Lorentz transformations

with a bunch of many other authors having historical variants of Lorentz transformations via Weierstrass coordinates, or via Cayley absolute, or via Cayley-Hermite transformation, or via Quaternions etc. (PS: Liebmann did indeed have the Lorentz transformations in 1905, which I initially overlooked). --D.H (talk) 21:44, 22 March 2018 (UTC)

The Mobius group has parabolic elements but the Lorentz group does not. I have begun to doubt the group isomorphism. — Rgdboer (talk) 03:16, 22 April 2019 (UTC)

Unblock

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Accept reason: It looks like collateral damage. I've unblocked you. Let me know if you have further trouble. NinjaRobotPirate (talk) 03:33, 1 October 2017 (UTC)

Thank you. — Rgdboer (talk) 02:42, 1 October 2017 (UTC)

History of logarithms

R, this version you wrote has a story similar to the one we just fixed at Napierian logarithm. The ref 13 doesn't appear to support what's said about this. Care to weight in on where to take this? Dicklyon (talk) 02:33, 13 May 2018 (UTC)

Please correct. That text was copied from Logarithm when History of logarithms was begun. November 24, 2015, the Logarithm article was seen to be too long, with much historic material. The namespace "History of logarithm" had a redirect to Logarithm, so text was moved to reduce Logarithm and begin an independent article. The prehistory of natural logarithm includes the story of Napier, but my efforts have been expended on A. A. de Sarasa and Gregoire de Saint-Vincent. While mathematics resists the notion of paradigm shifts, the invention of logarithms was revolutionary for productivity and setting up calculus. — Rgdboer (talk) 21:27, 14 May 2018 (UTC)

Relational view on functions

I just came here to express my wish/hope that you do not bother my use of your idea for these edits. Besides your unlucky use of a (typoed?) link, I shared D.Lazard's view of the original place not really being an optimal one. I expect that the new place and the reduced content might find grace in the eyes of the lords. It is beyond me to invite you to possibly add contents, according to your ideas (composition as another example?), but at least I want to say thanks for the trigger. Purgy (talk) 11:04, 7 September 2018 (UTC)

You’re welcome Purgy! Thank you for moving the material higher up the article. Editing on an frequently-viewed article is adventurous! But of course, relation is prior to function. — Rgdboer (talk) 02:19, 8 September 2018 (UTC)

Kutta condition

Hi Rgdboer. We are under siege at Talk:Kutta condition#"An aircraft with a wing with a smoothly rounded trailing edge would generate little or no lift.". If you are able to comment that would be appreciated. Regards. Dolphin (t) 13:21, 7 October 2018 (UTC)

A figure from flow separation was used to comment on lift (force) and use of potential flow. — Rgdboer (talk) 02:14, 9 October 2018 (UTC)

Many thanks for your contribution. I have commented on the Talk page.

I’m sure you are aware that potential flow is based on the assumption of zero viscosity, whereas flow separation occurs because of viscosity, so I find mention of both in the same sentence to be challenging. Dolphin (t) 12:25, 9 October 2018 (UTC)

Relevance?

In reading the list of Hotel Fires (List of hotel fires in the United States), I was struck by the abrupt introduction of what appeared to me as an irrelevant detail. I see that you added that detail on 2013 January 18‎ at 18:32, yet I don't see why.

It may be true that Lucius W. Nieman had become editor of a paper, but what does that particular detail have to do with Hotel Fires in general? I could see that that part could be rephrased to give similar info but without reference to Mr Nieman: A local newspaper (The Daily Journal) told the "appalling...

The fact that he had become the editor a few weeks prior to the fire leads to a belief that he was somehow responsible for the article about the fire, yet there is no clear connection nor even a clear indication of when that article was published. The rest of that paragraph, referencing the other newspapers in town doesn't seem to be relevant either.

Could you please readdress that article and see if the details can be either tied in to the topic or removed?

Thanks! WesT (talk) 18:00, 31 December 2018 (UTC)

The contribution has been re-written and moved to its section. The article has grown over six years, and that particular fire was recalled in a 1913 reference detailing other deaths on the Hotel's block. Nieman exploited the tragedy in his newspaper for gain, as noted by Scott Cutlip. In 2013 contributions to public relations and history of public relations led to the Cutlip observation. Thank you for calling attention to the Newhall house fire; the accent now is on the "death block" rather than media exploitation. — Rgdboer (talk) 00:28, 1 January 2019 (UTC)

Asking for clarification in an old entry

In Split-quaternion, when you created it in Feb 2007, there is something like this:

where u* = w - x i and v* = y - z i (complex conjugates of u and v), represents q in the ring of matricies in the sense that multiplication of coquaternions behaves the same way as the matrix multiplication. For example, the determinant of this matrix u u* - v v* = q q* ; the appearance of this minus sign where there is a plus in H leads to the alternative name split-quaternion for a coquaternion. Historically coquaternions preceeded Cayley's matrix algebra; coquaternions (along with quaternions and tessarines) evoked the broader linear algebra.

What do you mean by "H", I wonder.

用户名永远已存在 (talk) 19:47, 2 June 2019 (UTC)

Convention uses ℍ to designate quaternions, like ℂ for complex numbers and ℝ for real numbers. Will edit to clarify. Thank you for noticing. — Rgdboer (talk) 21:52, 2 June 2019 (UTC)

Use of INTDAB for disambiguation, August 23, 2019

An automated process has detected that when you recently edited Murphy, you added a link pointing to the disambiguation page Alex Murphy (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 07:42, 23 August 2019 (UTC)

Usually these notifications are deleted once the disambiguation has been made. In this case it can be left to show the bot's failure to comprehend that the Alex Murphy page should be on the Murphy page even when there are several people called Alex Murphy. — Rgdboer (talk) 20:53, 23 August 2019 (UTC)

Standard approach to this situation is described at WP:INTDAB, a Project convention. — Rgdboer (talk) 21:48, 28 August 2019 (UTC)

Conformal symmetry

Hello Rgdboer. The purpose of my edit on conformal symmetry that you just reverted was to start bringing some order to the noodle soup of articles on conformal symmetry, conformal map, conformal geometry, conformal group. There is much duplicated material there, and in my opinion we need one or two articles instead of four. What do you think? Sylvain Ribault (talk) 07:41, 9 October 2019 (UTC)

Noodle soup is a metaphor, hardly applicable. Why contract the Project ? A challenge in the topic is finding sources that acknowledge that hyperbolic angle is an invariant of Lorentz transformations. That fact makes conformal physics much more involved than the inversive geometry that started the subject. In this project Physics and Mathematics are largely merged (not for compactification), so sources can conflict due to silos in academia. Please refer to split-complex number and linear fractional transformation for mathematical understanding. As for the soup, sip slowly from the bowl edge as it’s very hot. — Rgdboer (talk) 22:46, 9 October 2019 (UTC)

Respond to edit on talk page

You undid two of my edits on Template: number systems without responding to my comments on the talk page. I think it's worth grouping the planar numbers together. Also, where are the dual-complex numbers listed as a hypercomplex system? They aren't listed anywhere. As such, I'm reversing the edit. --Svennik (talk) 23:44, 22 October 2019 (UTC)

This issue stems from Hypercomplex number#Two-dimensional real algebras. The discussion continued at Template talk:Number systems.— Rgdboer (talk) 00:32, 19 November 2019 (UTC)

Disambiguation link notification for January 18

An automated process has detected that when you recently edited Allegory (mathematics), you added a link pointing to the disambiguation page Group (check to confirm | fix with Dab solver).

(Opt-out instructions.) --DPL bot (talk) 10:05, 18 January 2020 (UTC)

November 2020

Hi Rgdboer! I noticed that you recently marked an edit as minor at Music and mathematics that may not have been. "Minor edit" has a very specific definition on Wikipedia – it refers only to superficial edits that could never be the subject of a dispute, such as typo corrections or reverting obvious vandalism. Any edit that changes the meaning of an article is not a minor edit, even if it only concerns a single word. Please see Help:Minor edit for more information. Thank you. Kj cheetham (talk) 18:48, 20 November 2020 (UTC)

The change was a disambiguation of musical performance to musical phrasing. My impression was that WP:Dab is a minor edit, but that may be wrong. The article WP:Dab does not indicate either way. Thank you for the notification and caution in marking an edit as minor is in order. — Rgdboer (talk) 04:46, 21 November 2020 (UTC)

It was the edit before that about 53 equal temperament I was thinking of. Happy editing in any case though! -Kj cheetham (talk) 09:44, 21 November 2020 (UTC)

bounded, negative, finite ordinals

A simpler version of the Russell idea you mentioned at Ordinals and its talk page, that does work adequately with the usual idea of ordinals, is to pre-pend a specified finite number of negative steps before the start point. E.g., begin counting at -17 rather than 0 or 1. This doesn't change the order type of any infinite ordinal, or finite ordinals if the definition of (the notation for) those is modified to mean the interval between the number and 0. The union of all such negative prefixes to the usual ordinals is not allowed, in that it violates well ordering, but particular cases are compatible with the standard language. 73.89.25.252 (talk) 20:19, 3 December 2020 (UTC)

Hello Somerville, Massachusetts, USA, yes, we clicked at Talk:Scientific notation#Order as a scale, not a number. The consequent doubly infinite sequence came up on another article. The issue has existed since Russell mentioned in The Principles of Mathematics the counting backward from any position in a progression. Perhaps he forsaw the study of luminosity of Campanus, planets, moon, and sun on the scale of Hipparchus. Your suggestion appeals as an accomodation of that situation in an order of magnitudes. But negative twenty-seventh magnitude for the Sun is at one astronomic unit, so a scale going closer to the sun, would call for another position for the zero. Admitting the doubly infinite is part of scientific notation, regardless of Georg Cantor. Indeed, the doubly infinite geometric progression 10ⁿ, n in Z, sections the positive reals for access. You are invited to become a WP:User.— Rgdboer (talk) 02:19, 7 December 2020 (UTC)

The accomodationist strategy is often used where allowing some kind of extension, but only a finite amount of it, does not qualitatively change things (e.g. field or ring extensions, coverings) but throwing in all the finite adjustments at once gives a different sort of creature that does not belong to the category of interest. Typical use case is where a finiteness condition appears, such as finite dimension, finite ascending or descending chains, well ordering. Or using "almost" to denote a finite number of exceptions.

The problem with allowing the infinite modifications is not that it's wrong or can't exist but that the category of allowed objects would lose nice properties in the name of inclusiveness. Literal "can't have nice things" so that the extension is allowed for its own sake. 73.89.25.252 (talk) 18:01, 7 December 2020 (UTC)

Indeed, the doubly infinite geometric progression 10^n sections the positive reals for access. The distinction between "ordinal number" (having levels or layers or a hierarchy), and "integer" as in the stuff of arithmetic, seems to be a matter of linguistic custom or historical tradition that is orthogonal to the scientific notation discussion. The problems with OOM as an integer approximation function to the logarithm are practical mathematical concerns. 1) that anything physically meaningful (invariant) for dimensionful quantities has to be a binary relation, i.e., based on a ratio; 2) that the specific binary relation "same OOM" does not reduce to a unary function; 3) that if you do take it to be a function of one variable, it becomes dependent on a choice of rounding scheme, so again non-invariant; 4) if you do fix a rounding scheme anyway, it has to be discontinuous, so that almost identical quantities "have different order of magnitude" if OOM is defined in such a way; 5) that log-scale is unnatural for OOM approximations, we want them to be on the same scale as the input. All this is why (6) cognoscenti use the binary relation and the unary convention hasn't caught on, except maybe for people who only teach (or are forced to learn-and-forget) the stuff rather than use it for real. I tried drafting a re-write of the order of magnitude article and it's quite a pain to start over. Probably easier to do a minor fix on scientific notation first. 73.89.25.252 (talk) 06:42, 8 December 2020 (UTC)

This is being discussed at the Decade talk page in case you are interested. 73.89.25.252 (talk) 01:27, 18 December 2020 (UTC)

Proposed deletion of 2 × 2 real matrices

The article 2 × 2 real matrices has been proposed for deletion because of the following concern:

See Talk:2 × 2 real matrices#This article must be deleted

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. D.Lazard (talk) 11:02, 8 February 2021 (UTC)

Nomination of 2 × 2 real matrices for deletion

A discussion is taking place as to whether the article 2 × 2 real matrices is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Wikipedia:Articles for deletion/2 × 2 real matrices until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article.

D.Lazard (talk) 10:20, 9 February 2021 (UTC)

The article, slightly edited, is available through Wikibooks:

• b:Abstract Algebra/2x2 real matrices

Readers may comment on linear algebra here. Rgdboer (talk) 04:16, 10 October 2021 (UTC) Rgdboer (talk) 04:26, 10 October 2021 (UTC)

Your edit of "transformation semigroup" 03:13, 3 October 2019‎

Hi: I somehow feel that your changes at 03:13, 3 October 2019‎ were adding confusion, if not wrong. You changed the explanation of "transformation" from "function" to "partial function", which seems to be in contradiction to the definition of "transformation semigroup" in the first sentence, which reads:

"a transformation semigroup (or composition semigroup) is a collection of functions from a set to itself that is closed under function composition."

It seems also in contradiction to a paragraph below:

"The set of all transformations of X is a transformation monoid called the full transformation monoid (or semigroup) of X. "

where the "full transformation monoid/semigroup" usually means the monoid/semigroup of all functions (e.g., in Howie's book), not partial functions.

Or did I misunderstand your edits? ALife (talk) 07:19, 22 February 2021 (UTC)

See Transformation semigroup. The reader was right, thank you. Link to Partial function now placed in next sentence. — Rgdboer (talk) 03:43, 22 February 2021 (UTC)

Looks good. Thanks. ALife (talk) 07:19, 22 February 2021 (UTC)

Proposed deletion of Abraham Cornelius Benjamin

The article Abraham Cornelius Benjamin has been proposed for deletion because of the following concern:

Not notable by WP:GNG or WP:PROF

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. – Fayenatic London 10:25, 14 April 2022 (UTC)

References to many reviews of his books were added; notability per Author. Rgdboer (talk) 04:37, 18 May 2022 (UTC)

The utility for mechanics was noted by Aleksandr Kotelnikov.

Do you have a source for "The utility for mechanics was noted by Aleksandr Kotelnikov."? I consolidating this history page: https://en.wikipedia.org/wiki/Cross_product#History — Preceding unsigned comment added by 'wɪnd (talk • contribs) 13:36, 17 May 2022 (UTC)

The thesis he wrote at Kazan University refers to cross product in its title. Reference entered in History today. Rgdboer (talk) 04:33, 18 May 2022 (UTC)

Great. :) Do you know if the paper is accessible somewhere in the Russian original, in a collection, translation, quoted, or otherwise a way to verify its content? I find nothing here https://zbmath.org/?q=ia%3Akotelnikov.a-p and a mention without source here: https://mathshistory.st-andrews.ac.uk/Biographies/Kotelnikov/ 'wɪnd (talk) 16:06, 18 May 2022 (UTC)

Going to All-Russian Mathematical Portal and entering 1895 and Kotelnikov generates an article in the University journal where screw theory replaces cross product in the title. Perhaps the thesis is the article, with some translator substituting cross product. The screw displacement at the heart of the theory is a sufficient generator of the Euclidean group E(3). Like the vector representation of the cross product, the screw displacement has a screw axis. It involves both a rotation about the axis and a displacement along it. I have not read Kotelnikov’s work, but this Euclidean kinematic motion (somewhat related to cross product) is another subject, so the sentence you note may be a misdirection, so it can be deleted.Rgdboer (talk) 17:10, 20 May 2022 (UTC)

Mention of Kotelnikov at Cross product#History has been removed as unverified.Rgdboer (talk) 03:38, 23 May 2022 (UTC)

Screw theory look fascinating! :) Thank you also for the pointer to All-Russian Mathematical Portal. That will help me research another article I'm working on: https://en.wikipedia.org/wiki/Moment_(physics)#History

I've heard that Chebychev and others might have played a role in the origins of moments in probability theory and statistics, but I haven't found any direct attestations. This might help. 'wɪnd (talk) 20:48, 23 May 2022 (UTC)

Questions regarding your use of "beam space"

Hi Robert,

In Rapidity, you introduced the notion of "beam-space" which is novel to me. For some time now, I have tried to find other references on this particular parametrization of the Lorentz transform and have not been successful. The nearest I have come is in some work by Garret Sobczyk where he makes use of a similar technique that he identifies as a novel type of spectral decomposition. In particular, I am interested in whether there is a "beam-space" version of (2+1) and (3+1) Minkowski spacetime. I have tried using a simple 3x3 matrix transformation, but I seem to be missing some crucial conceptual ingredients.

I have intended to contact you for some time on this topic, so I hope that I am not overly forward in writing directly to your wikipedia talk page. Please let me know if there is a better way to contact you (for instance, over email would be very convenient for me as well).

Sincerely yours,

John Fries Jqgatsby (talk) 22:41, 15 November 2022 (UTC)

Thank you for your interest in this topic. The answer in mathematics lies with the equivalence of binary quadratic forms xy and xx − yy . The points (x,y) satisfying the quadratic forms when set to 1 lie on hyperbolic curves. The latter is called the unit hyperbola as it has minimal radius 1 while the other, a standard hyperbola, passes closest to the origin at (1,1), a distance of square root of two. The natural logarithm was born from this standard, but the unit hyperbola is used with rapidity in spacetime. The equivalence of the two quadratic forms uses a linear transformation that moves the clock and meter-stick coordinates to the beam space. Perhaps the article on split-complex numbers, where the unit hyperbola replaces the unit circle, with its references 3 to 8 on spacetime interpretation, will be helpful. The stories of young Einstein imagining chasing light, and the two alternate directions, form a popular background to this topic. — Rgdboer (talk) 01:17, 16 November 2022 (UTC) Revised Rgdboer (talk) 04:02, 16 November 2022 (UTC)

Let’s stick to two dimensions here, relating temporal to spatial metrics. The linear transformation

$(x,\ t){\begin{pmatrix}1&1\\-1&1\end{pmatrix}}=(x-t,\ x+t)$ has determinant 2 so the equivalence at binary quadratic form does not apply.

Nevertheless, the connection of the two quadratic forms is made linearly, and the form xy occurs when the asymptotes of the hyperbola are the coordinate axes. In the temporal interpretation, they are the beams to the left and right from a given (here, now). — Rgdboer (talk) 01:10, 17 November 2022 (UTC)

See Squeeze mapping#Relativistic spacetime and Light-cone coordinates for this concept. — Rgdboer (talk) 02:24, 7 February 2023 (UTC)

Reference desk answer 23/09/23

Gregoire de Saint-Vincent noted in 1647 that rectangular hyperbolas are stable under squeeze mapping, so planar areas are preserved not only in the whole plane, but also under the hyperbola. Thus the hyperbolic logarithm developed a century before Euler’s exponential functions a^x.

The correct statement is $\log x=\int _{1}^{x}{\frac {dt}{t}}$ where t is a bound variable.

Here the case a>1 and b>1 is considered first so the areas extend to the right of x=1 and the integral is seen as the area over [1,x] and under the hyperbola xy=1. Using b as squeeze parameter,

$\log a=\int _{1}^{a}{\frac {dt}{t}}=\int _{b}^{ab}{\frac {dt}{t}}.$ Then

$\log b+\log a=\int _{1}^{b}{\frac {dt}{t}}+\int _{b}^{ab}{\frac {dt}{t}}=\int _{1}^{ab}{\frac {dt}{t}}=\log ab.$

The cases where one or both of a, b are in the unit interval are similar when signed areas are noted.

Copied here for ease of reference. Rgdboer (talk) 22:34, 26 September 2023 (UTC)

Your edit in Binary relation

In your recent edit in Binary relation, you changed "functional relation" to "univalent relation" in the definition of this type of relation. This change leaves many occurences of "functional" (in this article) without any definition. Also, there are many articles that contain "functional relation" and certinly some of them redirect to Binary relation. Please, fix these issues.

By the way, per WP:LEAST, it is not a good idea to redirect Univalent relation to Partial function, and I have reverted this. D.Lazard (talk) 12:55, 28 January 2024 (UTC)

IMO, "functional relation" must be restored in the article. However, this requires some care, as it appears that, depending on the author it may refer either to a function or to a partial function. D.Lazard (talk) 14:20, 28 January 2024 (UTC)

The term functional relation is fraudulent. The redirect has been proposed for deletion. Inclusion of the term at Binary relation is expected to be removed. — Rgdboer (talk) 22:28, 31 January 2024 (UTC)

You currently appear to be engaged in an edit war according to the reverts you have made on Relativity of simultaneity. This means that you are repeatedly changing content back to how you think it should be although other editors disagree. Users are expected to collaborate with others, to avoid editing disruptively, and to try to reach a consensus, rather than repeatedly undoing other users' edits once it is known that there is a disagreement.

Points to note:

1. Edit warring is disruptive regardless of how many reverts you have made;
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes and work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases, it may be appropriate to request temporary page protection. If you engage in an edit war, you may be blocked from editing. - DVdm (talk) 06:12, 13 March 2024 (UTC)