Talk:Cartesian coordinate system

Axes and number lines

I reverted this edit of Persianwise, with the edit summary Axes and number lines are two different sorts of specific lines. In turn, he reverted my revert with the edit summary Notoce: "axis" is a term that is commonly used for a number line in mathematics, and posted Axes are number lines. Are you familiar with the x-axis and y-axis? These are number lines that are denoted by the letters x and y, respectively. Please stop preventing the article from being improved. on my talk.

After that, I tried to get a compromise, but I was reverted again. Thinking about that, I got convinced that the use of (coordinate) axis for a number line is very uncommon. So, I'll revert the section § One dimensional to the old version where the word "axis" did not appear.

By the way, I'll revert the other edits of the same user for reasons given in the preceding thread and in my edit summaies. D.Lazard (talk) 14:29, 2 September 2023 (UTC)

In the same paragraph, it is stated: ‘A line with a chosen Cartesian system is called a number line.’ It should be clarified that any coordinate system, including Cartesian coordinate systems, have axes. A number line is essentially a one-dimensional coordinate system. If the number line isn’t considered an axis, then where would the axis be located? If you answer this question correctly, you would understand that number lines and axes are two different names referring to the same concept.

DO not make any unwarranted revertions.

Persianwise (talk) Persianwise (talk) 23:20, 17 September 2023 (UTC)

You have not provided any reliable source that uses "axis" to refer to a numbeer line. So, your edit is a personal opinion. This is called WP:original research in Wikipedia, and not allowed in articles per policy WP:NOR. D.Lazard (talk) 11:20, 18 September 2023 (UTC)

Every axis is a number line but not every number line is an axis; the two are not synonyms, and your edit incorrectly proposed that they are.

Almost every part of D.Lazard's most recent edit was an improvement. In my opinion, there are two exceptions: (1) the cn tag needs double curly braces instead of single curly-braces, and (2) I think the spelling out of the meaning of bijection (that each point corresponds to a real number and each real number corresponds to a point) was a less technical way of conveying the point, so is likely worth preserving. 100.36.106.199 (talk) 13:22, 18 September 2023 (UTC)

It is "Analytic Geometry" that Introduced "Coordinate Systems".

Analytic Geometry is the branch of mathematics that introduced the concept of Coordinate Systems. Euclidean or non-Euclidean Geometries, by themselves, do NOT use Coordinate Systems. Therefore, it would be more accurate to change ‘geometry’ to ‘analytic geometry’, as this is what analytic geometry entails.

D.Lazard's comment:

"analytic geometry is much too restrictive, as it may prevent people interested in computational geometry, physics, mechanics, astronomy, etc. to read this article (all know geometry, but many may not know analytic geometry."

is subjective and lacks meaningful content. It is, in fact, a fallacy.

He has been warned before on his talk page, and he is hereby warned again to cease any attempts to make unwarranted reversions and to stop introducing inaccuracies due to insufficient mathematical knowledge. Persianwise (talk) 22:47, 17 September 2023 (UTC)

It is not analytic geometry that introduced coordinates systems, but it is René Descartes, a long time before the term analytic geometry was coined. Moreover, it is not geometries but geometers that uses coordinates systems. This is documented in the article Geometry, where coordinates systems and analytic geometry are clearly mentioned as parts of geometry.

Please, stop using accusations ("fallacy" and "insufficient mathematical knowledge") for trying to support your personal views. Use WP:reliable sources, if you can. D.Lazard (talk) 11:11, 18 September 2023 (UTC)

You are again using a fallacy by playing with words.

When we say that a branch or field of science introduced (or uses) some concept, it implicitly states that someone (a mathematician, scientist, etc.) invented that thing by introducing (or using) that concept.

For example, the invention of analytic geometry is generally credited to René Descartes, who combined algebra and geometry by using the concept of coordinate systems. (Geometry, by itself, was known for many thousands of years before the invention of analytic geometry.)

Analytic geometry cannot exist without a coordinate system, which paved the way for using algebra alongside geometry.

Therefore, it is more precise to say "In analytic geometry, a Cartesian coordinate system ..." than "In geometry, a Cartesian coordinate system ...." This is because coordinate systems are used analytic geometry, but they are not used in all types of geometry.

Unlike what you said previously, precision is not restriction. In fact, precision is often necessary for clear and accurate description. Persianwise (talk) 00:52, 26 September 2023 (UTC)

Protected

I have fully protected the article for a short period so the edit warring can be resolved on this talk page. Please review WP:DR and seek assistance at a relevant wikiproject. If necessary, and per WP:DR, use an WP:RFC if necessary. I will watch this page for a while. Feel free to ping me or any administrator if the article is ready to be unprotected due to consensus here (remembering that WP:CONSENSUS is not unanimity). Johnuniq (talk) 09:43, 18 September 2023 (UTC)

It should be mentioned that the page Cartesian coordinate system is about a subject of mathematics. To edit a mathematical subject, like any other scientific field, one must have the proper knowledge. Without the proper knowledge, any attempt to edit or make changes leads to inaccuracies that would confuse and misinform the readers. Notice that the user D.Lazard, due to lack of sufficient mathematical knowledge, is haphazardly changing sentences and publishing:

Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized mathematics by providing the first systematic link between geometry and algebra.

The correct and precise statement should be:

Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized mathematics by combining algebra and geometry.

The explanation for this was presented on his talk page: User_talk:D.Lazard.

But then he replaced it with:

Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized mathematics by allowing the expression of every problem of geometry in terms of algebra and calculus.

This is wrong because calculus was not even invented at that time.

(Analytic gemetry invented by René Descartes in 1637] , but Calculaus was invented in 1665 by Isaac Newton.

The user is evidently not just initiating the edit warring but also is actively engaged in sabotaging the article and preventing further improvement to the article. He should be blocked from editing mathematical related pages.

More information regarding his other unwarranted reversions will be given. Persianwise (talk) 17:03, 18 September 2023 (UTC)

The talk page of an article is not the correct place to discuss other editors. The correct page is WP:ANI but please examine WP:BOOMERANG before thinking about that. It is very common for disagreements to occur at Wikipedia and participants must follow standard procedures to avoid sanctions. Handling disputes is covered at WP:DR. Do not mention other editors or their alleged shortcomings on this page. If you want independent opinions on the accuracy of what I have written, ask at WP:Teahouse. The point is that editors must focus on content not on contributors. Have you asked for opinions at the wikiproject (see headings at top of this page)? I have not done more than glance at the issue and will take no part in discussing what should be done. However, you might bear in mind that articles generally focus on current practice, that is, what do people mean when they talk about the Cartesian coordinate system now? Please do not reply to this: I just raised an issue for you to consider. I suggest starting a new section with a brief outline of what problem you see in the current article and what should be done to fix it, with a brief explanation. Then try to get other opinions per WP:DR. Johnuniq (talk) 04:41, 19 September 2023 (UTC)

"Allowing the expression of every problem of geometry in terms of algebra and calculus" may perhaps not be ideal wording, but the essential point is not invalidated by the fact that calculus had not yet been invented, any more than "the invention of the wheel has had revolutionary effects on transport, such as enabling the manufacture of motor cars" is invalidated by the fact that the motor car was not invented until long after the invention of the wheel. JBW (talk) 20:33, 20 September 2023 (UTC)

I find both first and second versions acceptable, but the third... It's too strong to assume that "every" problem of geometry is reduced to algebra and calculus. 慈居 (talk) 08:49, 21 September 2023 (UTC)

@慈居: Well, in the context of Cartesian coordinate "geometry" clearly means Euclidean geometry, and Euclidean space is isomorphic to linear algebra in a vector space over the real numbers, and therefore every proposition about geometry in Euclidean space can indeed be expressed as an equivalent proposition in real algebra and calculus That is what was said in the quoted passage, which refers to "the expression of every problem of geometry in terms of algebra and calculus" (my emphasis) which is certainly possible. That is true whatever you may have in mind when you refer to "reducing" every problem of geometry to algebra and calculus, and whether or not such "reduction" in your intended sense is possible. JBW (talk) 17:07, 21 September 2023 (UTC)

I think you made a fair point. Instead of a boring argument, I'd like to mention the Jordan curve theorem, which says that every closed curve partitions the whole plane into two parts. This looks trivial (despite its lengthy complicated proof), but it yields nontrival conclusions when it's applied to some crazy curves like the Hilbert curve. This is how the word "every" is powerful. Even for classical Euclidean geometry, there was a famous (meta-)problem asking whether there is a hyperbolic geometry, and certainly this is not something expressable only with algebra and calculus (at least with the method of coordinate geometry). So in my opinion, both three sentences make sense (as you have pointed out for the third one), but I'd pick the first two of them as the better choices. 慈居 (talk) 20:11, 21 September 2023 (UTC)

OK, prompted by your comments, 慈居, I have thought some more about this. What do we mean by algebra? My post above in effect treats "algebra" as including anything which can be expressed in terms of an algebraic structure (in this case a finite dimensional real linear algebra) but that is a dubious interpretation; for example the metric and topological properties of such a space are not usually regarded as "algebraic". One could argue about exactly what features are added to the situation by the words "and calculus", but again topological properties are not, I think, generally regarded as being part of calculus. Above, I took issue with your statement on the basis that the quote attributed above to D.Lazard (but I haven't checked that attribution) refers not to reducing every problem in geometry to algebra and calculus, but to expressing it as such, but on reflection I think I was wrong: that was based on an interpretation of "algebra" as "any property of an algebraic space", but that is an unhelpfully broad interpretation of the word. Indeed, your example is highly pertinent: it would be difficult to express the Jordan curve theorem in terms which could reasonably be regarded as belonging to algebra and calculus. In the context in which this appears in the article, it is probably reasonably true that the kinds of geometric properties considered at the time when Cartesian coordinates were introduced can be expressed in terms of algebra and calculus, but since the statement in the form in which it is given is not justifiable, on reflection I think probably the best thing to do is to remove the word "every". I therefore intend to remove that word once I have posted this message, but of course I will be willing and interested to read any arguments in favour of its retention. (Well, any arguments by anyone who comes anywhere near to knowing what they are talking about.) JBW (talk) 21:15, 21 September 2023 (UTC)

About "calculus": I used "calculus" instead of analysis, because it is known by a wider audience. However "analysis" would be a proper term since, AFAIK, it denoted initially Descartes's method of coordinates and led to the term Analytic geometry, before becoming an alternative name of calculus.

About Jordan curve theorem: This is not a good example, as it involves the concept of "continuous curve" which cannot be defined in terms of pure Euclidean geometry. I do not imagine a way to define continuous curves without using coordinates, at least implicitly.

Nevertheless, I agree with the removal of "every", which would require either a source or an accurate definition of "algebra and calculus". D.Lazard (talk) 09:54, 22 September 2023 (UTC)

I also agree with the removal of "every". By the way @D.Lazard, the Jordan curve theorem was not at all intended to be a good example, or even an example. It was to illustrate how an assumption can be unnecessarily strong with the word "every". 慈居 (talk) 10:36, 22 September 2023 (UTC)

Cartesian coordinate system

Moved from Talk:Persianwise

You are starting an WP:edit war for trying to impose the idea that "number line" is a synonymous of "axis". It is true that the axes of a coordinate system are number lines, but this does not mean that the words are synonyms. Otherwise, this would be said in number line. In any case, Wikipedia rule are that any new assertion like yours must be supported by a reliable source (in this case of elementary mathematics, a widely used textbook). Otherwise, it is forbidden to add the assertion, per the policy WP:OR.

Please, remember also that edit warring may lead to an edit block (see WP:Edit warring). D.Lazard (talk) 18:00, 30 August 2023 (UTC)

In mathematics, a number line and an axis are equivalent concepts. They are often used interchangeably and can be regarded as mathematically synonymous, but they are not considered synonyms in the dictionary.

You stated that

“It is true that the axes of a coordinate system are number lines.”

However, on your own talk page, you stated that

"A number line and an axis are two different things."

This is contradictory to mathematical facts. Your actions evidently constitute Edit warring, as you have repeatedly reverted my correct assertion that a number line and an axis are the same thing. If you continue to engage in this behavior, I will report you as a Disruptive user. Persianwise (talk) 21:42, 30 August 2023 (UTC)

I don't see the logic of what you say. A cat is an animal, but "cat" and "animal" are not the same thing. There is no contradiction there; nor is there any contradiction in what you quote D.Lazard as saying. JBW (talk) 15:52, 20 September 2023 (UTC)

Your use of analogy is not valid here. The fact that "not all animals are cats" is because the set of all cats is a proper subset of the set of all animals.

However, my assertion is that the set of all number-lines and the set of all one-dimensional coordinate systems are identical.

This mathematical fact is even visually evident if you draw a number-line and a coordinate system in one dimension, both on the same geometric straight line, on a piece of paper. You will notice that a number-line is exactly a one-dimensional coordinate system because the axis in the one-dimensional coordinate system coincides with the number-line.

So, there is a bijection between the set of all points on the number-line and the set of all points on the axis; hence, they are the same.

Otherwise, where do you think the axis and the number-line are located relative to the aforementioned geometric straight line? Persianwise (talk) 18:19, 20 September 2023 (UTC)

That is completely missing the point. You said that there was a contradiction between the statement that axes of a coordinate system are number lines and the statement that a number line and an axis are two different things. Whether it is or is not true that a number line and an axis are both the same thing does not have any bearing on whether or not the statement (whether true or false) that they aren't is inconsistent with the statement (whether true or false) that the axes of a coordinate system are number lines. And that is quite apart from the fact that there being a bijection between the elements of two sets is not at all the same thing as their being the same thing. If you really can't see those two points then you should probably not be trying to improve the logic of the treatment of mathematical topics in articles. JBW (talk) 19:15, 20 September 2023 (UTC)

For clarification, it should be noted that the set of real numbers is a Field. It is obvious that the structure of a number-line defined by the same operations of addition and multiplication makes the two isomorphic - See Isomorphism. To mathematicians, two isomorphic fields (or any other relevant structures) are the same thing.

Analogously, the same thing can be said about the axis (more precisely, the set of points on the axis, with the familiar operations).

So all three are isomorphic, there are no differences between them, except the naming. They are all the same thing! Persianwise (talk) 20:48, 20 September 2023 (UTC)

NOTE: By “This is contradictory”, I meant “This [the second statement] is contradictory [to the established mathematical facts] (and not to the first statement). Persianwise (talk) 21:07, 20 September 2023 (UTC)

Oh, Christ. if you are going to say things and then say you meant something completely different than what any reasonable person would have thought you meant, then I may as well give up even trying. JBW (talk) 21:18, 20 September 2023 (UTC)

“If you noticed, I had stated ‘a number line and an axis are the same thing’, but the other user had said ‘A number line and an axis are two different things.’ which was contradictory to my assertion, and to mathematical facts. When ambiguity arises, why not explain things further to make things precise to get rid of ambiguity? Isn’t that the right thing to do?” Persianwise (talk) 22:01, 20 September 2023 (UTC)

You are saying that the x-axis and the y-axis of a Cartesian coordinate system are the "same thing" since they are both isomorphic to the field of the real numbers, and thus they are isomorphic. However, these two axes are different, and thus they cannot be the same thing. D.Lazard (talk) 22:08, 20 September 2023 (UTC)

The main meaning of isomorphism is the assertion that two seemingly different things are actually the same thing, except possibly for the names of their elements and the way the operations defined on them work. This is an advanced topic, hard to grasp for those who lack in-depth mathematical knowledge. I suggest you read the topic on this page that I posted at 18:19, 20 September 2023 (UTC). Anyone can see how to visualize why a number line and an axis (in a coordinate system) coincide, both representing the real number system. If you cannot see it, it is then crucial to answer the question that was asked there:

“Otherwise, where do you think the axis and the number line are located relative to the aforementioned geometric straight line?” Persianwise (talk) 22:46, 20 September 2023 (UTC)

How kind of you to help Daniel Lazard by explaining to him ideas which you understand but which are beyond him because of his being one of "those who lack in-depth mathematical knowledge". What a pity that nobody thought to teach him some elementary mathematics before he started his career. Hmm. Or... JBW (talk) 13:36, 21 September 2023 (UTC)

Your response is not pertinent to a mathematical discussion. He was asked this question twice:

"Otherwise, where do you think the axis and the number line are located relative to the aforementioned geometric straight line?”

and you know he failed to answer it.

Can you supply an answer to the aforementioned question yourself?

One does not even have to be a mathematician to answer it.

What is your answer? Persianwise (talk) 20:46, 24 September 2023 (UTC)

Just in passing, there would be no edit war if either of you just stop. No point in blaming each other. It might help if one restore an old version in which there was no edit dispute and seek consensus through discussion. (That worked in a dispute between me and still, D.Lazard.)

The difference of "number line" and "axis" is similar to that of a set and a subset. Any subset is a set and a set is always a subset (e.g. of itself). But are they the same? But anyway, you two should clarify why this matters. 慈居 (talk) 20:50, 25 September 2023 (UTC)

End of the moved discussion

It does not need to be restated that a number line can be considered its own axis. This is (a) unnecessary and redundant, and (b) a confusing distraction. (It is also not a claim supported by the provided sources, both of which just said that a number line is a line with numbers on it, and that each coordinate axis of a Cartesian plane is a number line, which is not at all the same thing as saying that "axis" and "number line" are synonyms.) –jacobolus (t) 16:49, 8 January 2024 (UTC)

(comment moved here from user talk:jacobolus)

You stated that "neither of these sources supports this claim". You are wrong! Please read both of the cited references.

You also stated that bold text are distractions. They are not. Bold text is for emphasis.

Additionally, you stated that "axis is defined to mean the principal lines through the origin". It does not mathematically make sense as "principal lines" are not defined in mathematics.

Persianwise (talk) 17:25, 8 January 2024 (UTC)

To elaborate a bit, these sources (an "Anonymous LibreText" and "Lesson 28" by Curriculum Associates, LLC, neither of which has obvious authorship or really seems like a "reliable source" by Wikipedia standards) claim that "The rectangular coordinate system consists of two real number lines that intersect at a right angle. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis." and "When a horizontal number line and a vertical number line are lined up so that the 0s meet, a coordinate plane is formed. [...] The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The point where the x- and y-axes meet is the origin.", respectively. These sources are saying that, in the context of the Cartesian plane, each axis is a number line.

Neither of these sources makes any claim that a one-dimensional line is, per se, an "axis", or that the term axis is a synonym of number line. It would be logically supportable based on an n-dimensional definition, albeit trivial, to call a number line its own axis. But this is unnecessary to make explicit, and essentially nobody ever describes it that way in practice.

Aside: The word axis originates from the line which remains fixed for a spinning object like a wheel, lathe, or the Earth (related to "axle"). Later the sense was broadened to include discrete kinds of spinning such as reflection across a line in the plane ("axis of symmetry"). When there is only one line involved as the entire space, as in the case of the number line, a linear axis is entirely trivial; you can't spin or reflect anything about it, because there is nothing outside of it. In the context of a line, the only relevant kind of transformation is reflection in a point, but a point center of reflection is rarely if ever called the "axis" either. I'm not quite sure when the term axis first started getting applied to the lines in a rectangular coordinate system with one coordinate equal to zero. –jacobolus (t) 17:19, 8 January 2024 (UTC)

NOTE:The edit wars mentioned below, which initiated by user:D.Lazard and user:JBW, were already terminated by correctly asserting that the terms "number line" and "number axis" (or simply axis) are the same. These are the terminology used in mathematics. You (user:Jacobolus) are restarting the same edit-war. Even school pupils know that these terms are interchangeable.

Persianwise 21:33, 8 January 2024‎ (UTC)

@Persianwise You don't need to make your text extra large or colorful. The folks participating here are all capable of reading ordinary-sized black text. You still have not provided any sources which validate your claim. The two sources you did provide say something entirely different, as I explained. I don't know what you mean by "used in mathematics", but in a quick literature search (using Google scholar) I can't find any example of the term "axis" being defined to mean the same as "number line". –jacobolus (t) 21:42, 8 January 2024 (UTC)

From your statement that "the horizontal number line is called the x-axis," it logically follows that a number line is indeed an axis. Persianwise (talk) 22:04, 8 January 2024 (UTC)

"the horizontal number line is called the x-axis" is not Jacobulus's statement; it is a statement of one of your sources. The logical consequence of this statement is that some number lines are axes, not that all number lines are axes as you pretend. In any case, bolding your assertions do not make them true. D.Lazard (talk) 22:16, 8 January 2024 (UTC)

While I don't think any published sources are likely to say this explicitly, I think it would be defensible to say something along the lines of "a number line is its own axis", in the sense that as a one-dimensional affine space it can be said to have one coordinate axis, coinciding with itself. I just don't think this article benefits in any way from making this (rather pedantic) point. It's also not at all the same as claiming that the two terms number line and axis mean the same (which is not a defensible claim in my opinion). –jacobolus (t) 22:50, 8 January 2024 (UTC)

You said:

"It does not need to be restated that a number line can be considered its own axis."

You statement does not mathematically make any sense.

You said:

"each coordinate axis of a Cartesian plane is a number line".

Don't you realize that "coordinate axis" is another name for "number axis" or just "axis". All these terms that you think are different objects, are actually the same thing. They are mathematically synonyms. Persianwise (talk) 21:55, 8 January 2024 (UTC)

Please stop to repeat again and again the same assertions without any source or argument for supporting them. This is WP:Disruptive editing, and this is not accepted in Wikipedia. D.Lazard (talk) 22:22, 8 January 2024 (UTC)

Anyone with basic knowledge of mathematics, even school pupils, learns that "number line," "coordinate line," "number axis," and simply "axis" are the same mathematical objects. References supporting this fact were provided on the following webpage and were also mentioned on your talk page.

Special:diff/1178434751

• "3.1: Rectangular Coordinate System". Retrieved 3 October 2023. ... The horizontal number line is called the x -axis, ...
• "Understand the Coordinate Plane" (PDF). Retrieved 3 October 2023. The horizontal number line is called the x -axis,

Persianwise (talk) 23:03, 8 January 2024 (UTC)

These are the same two sources we have been discussing, which I directly quoted above; neither one of them says that that "axis" is a synonym for "number line". (Aside, neither one of these seems like a "reliable source" by Wikipedia standards. Neither one has a listed author, and neither seems to have been formally published.) Everyone here has well beyond a "basic knowledge of mathematics"; adopting a condescending tone is tedious and does not make your argument any more convincing. –jacobolus (t) 23:12, 8 January 2024 (UTC)

If someone lacks basic mathematical understanding, it's advisable for them to consult relevant expertise before editing articles in that field. It's Common_sense. Persianwise (talk) 23:25, 8 January 2024 (UTC)

"Each cow in the barn is a farm animal" does not mean that "cow" and "farm animal" mean precisely the same thing. –jacobolus (t) 22:43, 8 January 2024 (UTC)

For your information, in mathematics, definitions are bi-directional. The terms "coordinate line," "number axis," and simply "axis" refer to the same thing. In your statement, you are not defining the cow. You are merely saying where the cows are. Persianwise (talk) 23:14, 8 January 2024 (UTC)

"in mathematics, definitions are bi-directional" – This is not correct, but this is not really the place to argue about it. Perhaps take it up on a forum about logic or philosophy. "In your statement, you are not defining the cow." – that is true; neither of the quoted passages from the sources you cited is making a definition either. Let me give a more explicitly analogous example: Imagine I am standing in a barn with you, and I point to a cow, saying "the farm animal by the water trough is called a cow". Can you see how that is not the same as a statement that every farm animal is a cow? (And also not a definition of "cow" or "farm animal".) –jacobolus (t) 23:18, 8 January 2024 (UTC)

In mathematics, ALL definitions are bi-directional.

Number lines are by definition are number axes. And number axes are number lines. Persianwise (talk) 23:29, 8 January 2024 (UTC)

"Number axis" is not a common term in English. A search turns up mostly results from Russian or Chinese sources, for example "Approximate solution of hypersingular integral equations on the number axis" (in Russian, where "number axis" is translated from "числовой оси"). –jacobolus (t) 23:54, 8 January 2024 (UTC)

Hmm, how about a "set" and a "subset"? Every subset of a set is a set, and every set is a subset of some other (e.g., of itself). Does that make sets and subsets the same thing for you? 慈居 (talk) 00:01, 9 January 2024 (UTC)

If isomorphic objects (some of which might be, e.g., disjoint) are the same, what about categorically equivalent objects? Is it acceptable to you to say that a group and a non-group (e.g., a groupoid) might be the same? 慈居 (talk) 00:05, 9 January 2024 (UTC)

I think these distinctions are a bit beyond the level of conversation we're engaged in here. Overall, this thread seems like a waste of time.

@Persianwise why don't you come back when you have (a) some sources which actually support your claim, and also (b) a more collaborative attitude, with some willingness to listen and learn from other people? In the mean time, please stop with the edit warring. –jacobolus (t) 00:10, 9 January 2024 (UTC)

I agree; can't believe this goes again. 慈居 (talk) 00:18, 9 January 2024 (UTC)

Number axis is a term used in elementary mathematics with the same meaning as number line. Although mathematical definitions are universally valid and transcend language, their presentation can vary across educational levels. My references from secondary school websites naturally reflect terminology introduced at that stage, even though the concepts behind number line and number axis are synonymous and readily grasped by most. Therefore, including a clarification within the article about the interchangeable use of these terms would benefit those encountering them across different educational resources, even those less mathematically inclined. This concise explanation should dispel any potential confusion and enhance the reader's understanding. Persianwise (talk) 01:55, 9 January 2024 (UTC)

If you disagree with my assertion that "number line" and "number axis" are synonyms, I encourage you to review the reputable secondary school resources I cited, or relevant mathematical literature that clarifies their equivalence. Persianwise (talk) 02:03, 9 January 2024 (UTC)

You were previously blocked over this. Coming back months later to restart the same issue is not a good idea. Time to WP:DROPTHESTICK Meters (talk) 02:04, 9 January 2024 (UTC)

@User:Meters Your statement lacks mathematical content. Do you concur with user:D.Lazard, user:JBW, and user:慈居 in asserting that "number line" and "number axis" are distinct objects? Persianwise (talk) 02:16, 9 January 2024 (UTC)

I have bothered to give you a mathematical content and yet expecting an answer from you. Why are sets and subsets different concept with your logic? 慈居 (talk) 02:55, 9 January 2024 (UTC)

@user:慈居 Your question, even if assumed to be correctly stated, is irrelevant to the issue caused by the edit war initially started by user:D.Lazard, and user:JBW and then restarted by user:jacobolus. Please stay on topic.

Do you disagree that "number line" and "number axis" are the same thing? Persianwise (talk) 08:49, 9 January 2024 (UTC)

That depends on what you mean by "the same"; you are free to define it whatever you like, but they don't apply to others. 慈居 (talk) 10:01, 9 January 2024 (UTC)

1+1 is the same as two. Obviously, number lines are number axes; they are the same. Any other question? Persianwise (talk) 15:55, 9 January 2024 (UTC)

Just chiming in to concur that Persianwise has not convinced me. All squares are rectangles, but not all rectangles are squares. All axes may be number lines, but it does not follow that all number lines are axes. EducatedRedneck (talk) 17:19, 9 January 2024 (UTC)

I'm just chiming in to note that Persianwise has been blocked indefinitely for continuing to edit war after having been previously blocked for it. Wikipedia is not a game to be won - we settle disputes by constructive discussion, not by wearing down opponents with legalesque interrogation and thinly-veiled insults. Ivanvector (^Talk/_Edits) 17:42, 9 January 2024 (UTC)

The basic definition here should be broader, not requiring perpendicular axes or equal spacing on different axes

The name "Cartesian coordinates" is commonly applied (both in basic textbook definitions and in practical use) not only to coordinates in square grids in Euclidean space, but also more generally to coordinates on rectangular or parallelogram grids, including in general affine space or real coordinate space where the concepts of perpendicularity and distance may not be defined. Such broader definitions can be found in many sources, and are in wide use, so our restrictive definition here may be misleading to readers. In my opinion in this article we should make a definition which is general and discuss the possibilities, while also mentioning that some authors have square grids in mind when they say "Cartesian coordinates" (and we can give extra attention to this common special case). –jacobolus (t) 18:06, 16 October 2024 (UTC)

As far as I know, "Cartesian coordinates" generally refers to coordinates with respect to an orthonormal basis. When the basis is not orthonormal and when orthogonality is not defined, one talks of affine coordinates. However, if one finds a source supporting the following sentence, I would not oppose to add to the lead a sentence such that When orthogonality is not defined and when the coordinates axes are not orthogonal, affine coordinates are defined similarly and called also "Cartesian coordinates" by some authors. D.Lazard (talk) 20:30, 16 October 2024 (UTC)