User talk:Kamil Kielczewski

Hi I see you are interested on HSL and HSV can you help here https://gitlab.gnome.org/GNOME/gimp/issues/427

Nomination of Matrix representation of tensors for deletion

A discussion is taking place as to whether the article Matrix representation of tensors 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/Matrix representation of tensors 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. Jasper Deng (talk) 08:21, 19 February 2020 (UTC)

Why I removed most of your edits

Please don't take it personally, but you need to supply reliable sources for any and all content you add, such as the derivation of the Cauchy momentum equation. The ones you used in Matrix representation of tensors don't cut it --Jasper Deng (talk) 09:56, 19 February 2020 (UTC)

February 2020

Your recent editing history at Divergence shows that you are currently engaged in an edit war; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See the bold, revert, discuss cycle for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

Being involved in an edit war can result in you being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.
This isn't how it works: you need to establish the verifiability before re-adding the disputed content. Jasper Deng (talk) 21:25, 19 February 2020 (UTC)

Source

Please do not add or change content, as you did at Imaginary unit, without citing a reliable source. Please review the guidelines at Wikipedia:Citing sources and take this opportunity to add references to the article. Thank you. - DVdm (talk) 11:15, 22 July 2020 (UTC)

@DVdm: I take this source from other wikipedia aricle https://en.wikipedia.org/wiki/E_(mathematical_constant)#cite_note-OConnor-5 (!!!) - can you explain what is wrong with it and fix that article which also use that source? — Preceding unsigned comment added by Kamil Kielczewski (talk • contribs) 11:30, 22 July 2020 (UTC)

It's not because some other article cites a poor source, that this article should do the same — see wp:OTHERSTUFFEXISTS. Can you find a proper book source for this edit? - DVdm (talk) 11:34, 22 July 2020 (UTC)

@DVdm: I don't have other sources - so I think you should also fix that: https://en.wikipedia.org/wiki/E_(mathematical_constant)#cite_note-OConnor-5 article If you claim that source is bad (otherwise people will be misled like me) - unless you have double standards... — Preceding unsigned comment added by Kamil Kielczewski (talk • contribs) 11:45, 22 July 2020 (UTC)

Please sign all your talk page messages with four tildes (~~~~) and indent the messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.

Ok, done: [1]. If indeed there are no book sources for this, and this website is the only source in the world, then the content is unlikely to be wp:noteworthy for Wikipedia. - DVdm (talk) 12:05, 22 July 2020 (UTC)

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Functions

Due to some deadlines, I must be brief. You may find the following comments helpful.

Your "triple proposal" can be salvaged by distinguishing between a triple a, b, c (which can be seen as a function, the argument being an index), and a triplet where the triple A, B, f is put between angle brackets exclusively used to represent a labeled function with source A, target B and function (in the ordinary sense) f.

Also, for selectivity, the qualification of surjectivity or ontoness is best viewed as a relation between a function and a set, such that "f is surjective on Y" and "f is onto Y" and "the range (or image) of f is Y" are equivalent statements.

The references can be found by clicking "show" on the green rectangle in the "Function" talk page, or on my own user page. Page 856 on [2] may also be informative. Your reference to Mayer is interesting: it is one of the very rare calculus texts that use codomains, yet is wise enough to essentially ignore them when defining function composition, but still runs into trouble with function inverses in the manner explained by Shuard in 1976 ([3] paper "Does it matter") Boute (talk) 08:12, 1 March 2024 (UTC)

Thank you for this information - I also have little time but will gradually familiarize myself with your material.

I have a first question: In [2] (you provided the link) it is written: "a codomain refers to the set Y in a triplet <f,X,Y>...In calculus, codomains cause problems as noted in [15]" where [15] is H. S. Shuard, Does it matter?, Math. Gaz., 59 (1975), pp. 7--15. I found this article here:

https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/does-it-matter/97BF3C1B393460C448D6BA551036C0FB

but unfortunately, I do not have access - and I am curious about what specific problems the triplet codomain causes in calculus. Do you perhaps have the rights to view this article and could you quote me a passage regarding the said problem? Kamil Kielczewski (talk) 15:01, 1 March 2024 (UTC)

Pity, a few years ago the article was easier to dig up. So here is the literal quote from Shuard.

(begin quote) The only analysis book I know, that by Sprecher, which uses the domain-codomain definition, gets into difficulties later on, with the sentence

"Given a set A and a continuous one-to-one function f : A -> Reals, then this f has an inverse f^{-1} : f(A) -> A"

(Shuard continues) Strictly, the function f : A -> Reals does not have an inverse finction on Sprecher's definition unless f(A) = Reals, ...(end quote)

Shuard last remark is also relevant to Mayer's inverse (definition 14.21), which requires the domain of the inverse to be the codomain of f.

(end quote)

Shuard is not always careful, for instance when saying that Flett does not care about ontoness, but actually Flett uses onto as a preposition, saying "onto Y". She also admits that "Flett's definition wins hands down as far as simplicity in analysis is concerned." (right on) but continues with "In Algebra, however, it is more convenient to start by mentioning the codomain of a function, since we are usually interested in functions which, for instance, map one group into, or onto another". Yet, with "onto" as a preposition, this is evident, no codomain needed.

A personal aside: over the past 30 years, I regularly have asked mathematicians why some people might want codomains, but the best answer I ever got was: "tradition in some areas of mathematics". Halmos observes that , in mathematics, "tradition always conquers pure reason". Boute (talk) 16:25, 1 March 2024 (UTC)

Thank you, I will think about this some more. As for the last question related to the use of codomains, from what I've heard, topologists need them... Kamil Kielczewski (talk) 16:45, 1 March 2024 (UTC)

Meanwhile I found a way to retrieve Shuard's paper.

[4]

there you can read 100 papers per month for free. Let me know if this succeeds.

For topologists, 'need' is relative. It may be tradition, or just a fashion, perhaps due to not using "onto" as a preposition, as "analysts" do. James Munkries's in "Topology", page 16, talks about f : A -> B , calling A the domain of f and B the range of f (what others call codomain!), and mentions that "analysts avoid giving B a name". All this is just terminology, but the real loss appears on p. 17 where composition is defined only for f : A -> B and g : B -> C, not for any functions f : A -> B and g : D -> E, as needed to do calculus properly (e.g. the chain rule).

Serge Lang in "Undergraduate Analysis" (an exemplary book otherwise) says on p. 5 that a function f : S -> T is "onto T" if its image/range (in the usual sense) is T, but then misses a golden opportunity in using the term "surjective" (without mentioning "on T") as a property of the function. This forces him to consider T a property of f (without calling it a codomain), with immediate penalty: composition (p. 7) defined only for f : S -> T and g : T -> U, but when he reaches the chain rule (p. 63) he is forced to sweep this under the carpet, requiring only that the image/range of f is a subset of the domain of g (still unnecessarily restrictive). Boute (talk) 18:15, 1 March 2024 (UTC)

Thank you for your kindness Kamil Kielczewski (talk) 07:20, 4 March 2024 (UTC)

March 2024

Please do not attack other editors. Comment on content, not on contributors. Personal attacks damage the community and deter users. Please stay cool and keep this in mind while editing. Thank you. MrOllie (talk) 14:25, 14 March 2024 (UTC)

@MrOllie Ok, I accept this warning - but for instance please tell me what you think about such a statement from this person at 16:42, 3 March 2024 here:

"I strongly disagree with everything you could write on this subject"

In my opinion, such an attitude is contemptuous, hostile, and does not at all facilitate a substantive exchange of views. This is partly where my opposition to the actions of this person stemmed from. Kamil Kielczewski (talk) 14:50, 14 March 2024 (UTC)

I'm not going to debate other people's comments with you. Focus on what you can control - your own writing. MrOllie (talk) 14:51, 14 March 2024 (UTC)

ok Kamil Kielczewski (talk) 14:52, 14 March 2024 (UTC)

Ordered pair

Hi, I copied your proof box from ordered pair since I have some questions - even if the box has been deleted. I inserted my comments in your text.

Note regarding the symbol $\pi _{1}$ (it is not a function).

The symbol $\pi _{1}(p)$, meaning the projection of the first element of a pair, is not a function within the framework of ZFC. This expression only has symbolic significance. Proof: By definition, a function is a set of pairs, so if we assume that the function $\pi _{1}$ exists, then $\pi _{1}=\{(p_{1},a_{1}),(p_{2},a_{2}),....\}$. Next, we can construct a pair $p_{1}$ containing this function in the first element, e.g., $p_{1}=(a_{1},b_{1})=(\pi _{1},0)$. Then, the result of applying the function $\pi _{1}$ to the pair $p_{1}$ would be:

$\pi _{1}(p_{1})=\pi _{1}((\pi _{1},0))=\pi _{1}$

Using Kuratowski's definition of a pair, $p_{1}=\{\{\pi _{1}\},\{\pi _{1},0\}\}$ and $(p_{1},\pi _{1})=\{\{p_{1}\},\{p_{1},\pi _{1}\}\}$. Thus, we can write:

$\pi _{1}\subset \{\pi _{1}\}\subset p_{1}\subset \{p_{1}\}\subset (p_{1},\pi _{1})\subset \pi _{1}$ [1: Every "$\subset$" should be "$\in$", shouldn't it?] [2: I can see a justification for every $\in$ relation, except for the very last one. Where did you get that one from?]

This means that the set $\pi _{1}$ is an element of itself at some level of nesting, which is not possible within the framework of ZFC (no infinite descending sequence of sets exists - Axiom of Regularity). A similar situation occurs for below $\pi _{2}$ symbol.

Best regards - Jochen Burghardt (talk) 15:12, 30 July 2024 (UTC)

@Jochen Burghardt

1. You are right should be $\pi _{1}\in \{\pi _{1}\}\in p_{1}\in \{p_{1}\}\in (p_{1},\pi _{1})\in \pi _{1}$

2. I wrote "By definition, a function is a set of pairs, so if we assume that the function $\pi _{1}$ exists, then $\pi _{1}=\{(p_{a},a_{a}),(p_{b},a_{b}),....\}$" (I use letter indexes instead numbers to avoid confusion) - where $(p_{x},a_{x})=((a_{x},b_{x}),a_{x})$. Because $\pi _{1}(.)$ should work with any pair - then it should also wrok for pair $p_{1}=(\pi _{1},0)$. This means that pair $((\pi _{1},0),\pi _{1})=(p_{1},\pi _{1})$ must be element of our set (function) $\pi _{1}$ (otherwise the function would not have a defined value for the pair $p_{1}$). Did that clarify things a bit? If not, let me know and I'll try to explain it differently. Kamil Kielczewski (talk) 18:32, 30 July 2024 (UTC)

Many thanks; I think I understood it now. I'd write the "$\in$" chain with explanations interleaved, e.g. like this:

${\begin{array}{lll}&\pi _{1}\\\in &\{\pi _{1}\}&{\mbox{ by Def. of set comprehension}}\\\in &\{\{\pi _{1}\},\{\pi _{1},0\}\}&{\mbox{ by Def. of set comprehension}}\\=&p_{1}&{\mbox{ by Kuratowski Def. of }}p_{1}\\\in &\{p_{1}\}&{\mbox{ by Def. of set comprehension}}\\\in &\{\{p_{1}\},\{p_{1},\pi _{1}\}\}&{\mbox{ by Def. of set comprehension}}\\=&(p_{1},\pi _{1})&{\mbox{ by Kuratowski Def. of }}(p_{1},\pi _{1})\\\in &\pi _{1}&{\mbox{ since the first projection of }}p_{1}{\mbox{ is }}\pi _{1}{\mbox{ by construction}}\\\end{array}}$

- Jochen Burghardt (talk) 11:11, 31 July 2024 (UTC)

your veriosn looks quite clear I'd say Kamil Kielczewski (talk) 11:17, 31 July 2024 (UTC)