Talk:Variable (mathematics)/Archive 1

Archive 1

Statistics

I think the section on variable in statistics is significant enough that it could be split into its own article (variable (statistics)). Thoughts? --_{Piotr Konieczny aka Prokonsul Piotrus| talk} 21:36, 25 May 2010 (UTC)

Although I know little about these matters, it would be my guess that the use of variable in statistics is much closer to the notion of random variable from probability than to the notion of variable elsewhere in mathematics; notably it seems to me more like a function that a variable. I agree this article should not be about variable in probability and statistics, though it should refer to those notions. Marc van Leeuwen (talk) 07:42, 26 May 2010 (UTC)

Removing History section

I traced the section to the original version (at least the oldest version stored) of the article X. This was expanded in this edit. This refers to the use of X as a a symbol for an unknown quantity, not a variable in the sense used in this article. Even if the section is accurate as a history of X, which is questionable since it's unsourced, it's referring to a subject different from the subject of the article and so I'm removing it.

No and yes. Its closing sentence: "That started the habiyt of using letters to represent quantities in algebra." In other words, the purpose of that passage is to explain how variables were introduced in mathematics. But indeed, a source for those statements should be added. 131.155.69.240 (talk) 16:05, 24 September 2010 (UTC)

"unknowns" vs. "unknown quantities"

The article introduce the term unknown and 2 lines later asserts in some languages other than English, one distinguishes between "variables" in functions and "unknown quantities" in equations, which means that the distinction between variable and unknown does not exists in English. This is a contradiction not only by itself but also with the practice of most English writing mathematicians. A correction is needed. D.Lazard (talk) 18:29, 18 December 2011 (UTC)

I removed the bit about foreign languages. Honestly though, most of the article is unreferenced and apparent OR so it's hard to get too excited about a measly contradiction or two.--RDBury (talk) 17:01, 19 December 2011 (UTC)

Merge proposed (again)

Both Constant (mathematics) and Variable (mathematics) describe variable vs. constant in the lead. It would be natural to describe them in one article just as Dependent and independent variables or Free variables and bound variables are described in one article, because a constant is defined in contrast to a variable and vice versa. The name of the new article could be Constants and variables. Isheden (talk) 19:20, 29 September 2013 (UTC)

• I support the merge, but, in my opinion the new article must be named "variable". In fact, in modern mathematics, and specially in algebra, the word "variable" has lost its original meaning of "may vary" and simply denotes a symbol representing a mathematical object. As quoted in the last sentence of the lead, the distinction between "variable" and "constant" depends on the point of view. For example, when the quadratic polynomial $ax^{2}+bx+c$ is considered as a defining a function or an equation, a, b, c are constants and x is a variable. On the other hand, when considering the vector space of the quadratic polynomials, a, b, c are variables, and x is a constant (the constant element x of the polynomial ring). D.Lazard (talk) 21:24, 29 September 2013 (UTC)

• I don't support the change. Although the definitions of the two concepts are really the same distinction seen from opposite sides of the fence, once you get beyond the initial definition you are dealing with different matters. it wouldn't be an unmitigated disaster if the articles were merged, but I really don't see that it would be an improvement.
• On the separate issue raised by D.Lazard,however, I strongly oppose the suggestion. It may be that I am just hopelessly old fashioned, but I have always regarded the word "variable" as referring to something which may take a range of values, not as just "a symbol representing a mathematical object". It is true that some people, particularly those of moderate mathematical understanding, do not grasp the differences in usage of letters in different contexts, but that doesn't mean that mathematics doesn't draw a distinction. Of course D.Lazard is right in saying that, in ax² + bx + c, whether a, b and c are constants or variables depends on the context, but that in no way detracts from the fact that in a particular context there is a clear difference between the two concepts. Perhaps modern mathematical usage has moved on, leaving me behind, and the word "variable" now means any letter or symbol representing anything, but I would like to see evidence that it has. I also think that D.Lazard is making a mistake which is all too common among mathematicians who edit mathematical articles, namely approaching the subject from too advanced a point of view. It is highly unlikely that anyone with any notion of what "the vector space of the quadratic polynomials" is would be looking at either of these Wikipedia articles to find out what "variable" or "constant" means, but it is perfectly likely that someone at a much more elementary level would do so. From the point of view of such a reader, there is a fundamental difference between the x and the other three letters in ax² + bx + c, which many learners find difficult to grasp, and it is far more likely to be helpful such a reader to make that distinction clear than to blur it. The minority of those readers who subsequently go on to a higher level of mathematical understanding will have the opportunity to realise that the variable/constant distinction is context-sensitive, and their understanding is unlikely to have been impaired by an early introduction to the idea that they are distinct concepts. I have known people say that they frequently consult Wikipedia for information on many subjects, including sciences, but not mathematics, because the mathematical articles are written from a too advanced perspective, making them very difficult for even an intelligent non-mathematician to understand, and this, I think, is a good example of why. JamesBWatson (talk) 11:56, 1 October 2013 (UTC)

I apologize to have been influenced, in my previous post by the rise of computer science and in particular of computer algebra. It would be better to make this explicit. I would fully agree with JamesBWatson's comments, if computer science and computer algebra would not exist. But, this article has to take into account that many readers of this article have certainly used some programming language and/or computer algebra system. Thus the definitions that are given should not be contradictory with those of these fields. Some programming languages have a distinction between constant and variable, but there is nor semantic difference; this distinction is purely technical and occurs only for the needs of the compilation. In computer algebra, variable means exactly what I have said, namely the name of any object represented in the memory. As more and more people, which learn mathematics, are experimenting on computer algebra systems, even at a very low level, it seems important to give definition that are not confusing for them. By the way, I have experienced that the disastrous habit of many teachers of using systematically the functional notation for denoting the polynomials (Let p(x) be a polynomial...) is highly confusing for most beginners in computer algebra, making very difficult to understand the difference between an expression and a function (which, in computer algebra, is nothing else than a program). D.Lazard (talk) 15:15, 1 October 2013 (UTC)

OK, thanks for explaining that. I now have a much better understanding of what you had in mind. However, the title of this article is Variable (mathematics), and the simple fact is that in mathematics, unlike computer programming, the two concepts are distinct. Indeed, I would go so far as to say that the fact that computer programming languages use the term "variable" differently to how mathematicians use the term makes it even more important to make the distinction clear in articles relating to mathematics. People who have come across the term "variable" in computing, and learnt what it means, and then come across the same word used in a different sense in mathematics may well be misled or confused unless it is made clear to them that the word is being used in a different sense than the one they have come across elsewhere. If they turn to Wikipedia and see that in connection with mathematics there is an account that makes it seem that the word has the same meaning as in computing, that is likely to increase the risk of being misled or confused. If, on the other hand, they see that the account of the word in connection with mathematics gives a different meaning, it is likely to help them to understand the meaning of the word in connection with mathematics. I therefore see your argument as totally upside down: the fact that the word is used differently in computing is all the more reason to make the distinction clear, to avoid confusion, not all the more reason to blur the distinction, adding to the risk of confusion.

I have several thoughts in relation to your comments about polynomials, but it seems off-topic, so I will not expound on them. However, I do see that, as with your comments about "variable", you seem to think that mathematicians for some reason ought to allow our usage to be dictated by the convenience of computer programmers, an opinion with which I don't agree. JamesBWatson (talk) 19:12, 1 October 2013 (UTC)

I believe that you have misunderstood my point. It is not that the mathematical usage should be "dictated" by the convenience of computer programming. The point is that more and more mathematics is done and will be done on computers. This has already deeply changed many things in mathematics. One of the important changes is that much more accuracy is needed for expressing mathematics, because computers do not accept approximate wordings. An example, not far of our subject, is the notion of expression which is formally defined only since expressions are used and manipulated in computers. Every formal definition of "expression" includes the definition of "variable", but I do not know any mathematical (that is formal) definition of "variable" vs. "constant". Without any mathematical definition I do not see how the distinction between variable and constant may be considered as a mathematical concept. However, I agree that this distinction is useful to explain the relationship between abstract mathematics and the reality that it allows to describe. As there is only one true mathematical concept, having two separate articles is a mess. D.Lazard (talk) 22:28, 1 October 2013 (UTC)

Based on the discussion here and above (where a merge was first proposed), I'd like to summarize as follows and then make a new proposal. An article about constants and variables must be accessible to lay readers. Constants and variables are naturally defined in contrast to each other and it is not really useful to have two different articles that discuss the variable vs. constant dichotomy. Hence, a reader who is looking for that discussion should be redirected here, although changing the title of this article is not needed. What speaks against merging is that the word "constant" has more meanings in mathematics, including mathematical constant, constant function, constant term, and constant of integration. But, as detailed on the page Talk:Constant (mathematics) I think it would be better to reduce Constant (mathematics) to a disambiguation page with links to the other articles rather than having an article of low quality trying to cover all of them just because they are called something with "constant". One possibility is to redirect Constant (mathematics) to Variable (mathematics) and put a "Constant (mathematics) redirects here. For other uses, see Constant" hatnote at the top of this article. Isheden (talk) 08:02, 2 October 2013 (UTC)

• I support this new proposal, which looks very fine. D.Lazard (talk) 12:45, 2 October 2013 (UTC)

Merge Constant (mathematics)

Constant (mathematics) is currently an unsourced stub with little information. The variable vs. constant dichotomy is already discussed in this article so it seems natural to simply redirect the Constant article here.--RDBury (talk) 21:45, 26 September 2010 (UTC)

Would that require renaming this article to reflect the inclusion of Constant? --Cybercobra (talk) 21:58, 26 September 2010 (UTC)

Constant is a disambiguation page so the link could just be changed there.--RDBury (talk) 03:59, 27 September 2010 (UTC)

I think you've misunderstood me. I meant "In the event of such a merge, should Variable (mathematics) be renamed to e.g. Constants and variables or similar?". --Cybercobra (talk) 04:26, 27 September 2010 (UTC)

I oppose a merge, since Constant (mathematics) gives a very simple explanation (the polynomial example) for the lay reader. --JaGa^talk 08:55, 27 September 2010 (UTC)

Oppose Though constant (mathematics) is currently low on content, it may become a better article in time, and should not be merged with this one. Furthermore, it is not true that "constant" is simply an antonym for "variable". For example, it is common to talk about a constant term or constant function, but one does not usually discuss "variable terms" or "variable functions". There are also constants of integration, which deserve to be mentioned in an article on constants, but would have no place here. Jim.belk (talk) 01:23, 14 November 2010 (UTC)

Oppose, they are two totally different concepts, and therefore should each have their own article. —Preceding unsigned comment added by 85.210.189.220 (talk) 23:12, 1 April 2011 (UTC)

Oppose, they are related concepts but entirely different. Cross-linking should be encouraged. — Preceding unsigned comment added by 85.119.21.2 (talk) 08:51, 8 October 2013 (UTC)

General Comment on this article

Is the purpose of this article for writers to show readers how much they know about variables (whilst revealing how little they know about communicating); is it here to help readers learn what variable are and how they are used; or does the article have some other purpose, one that I a have not discerned? I know what a variable is. I started learning about what variables are, and how they are used, about 50 years ago, and have used variables just about every day since then. I came here hoping to get some ideas about how to best explain to my grandchildren, what variables are and how they are used. So as I read the article I asked myself, if I didn't know what variables are and how they are used, could I get the answer from this article? The answer to the question that I asked myself, is no. I hesitate to try and edit the article because in the past other editors frequently removed my clear explanations and restored the previous vague, ambiguous, or erroneous explanations.

Nomenclator (talk) 19:51, 25 October 2013 (UTC)

As to what the purpose of Wikipedia mathematics articles is and is not you can have a look for example at Wikipedia:Manual of Style/Mathematics and Wikipedia:What Wikipedia is not. How would you like to improve the article? Isheden (talk) 21:57, 25 October 2013 (UTC)

New lead

The previous lead defined the notion of variable only in the context of elementary mathematics, and did not took into account that "variable" has different meanings which are context dependent. Moreover, it insisted that "variable" must be able to vary, without giving a mathematical definition of this variability (in fact such a definition does not exist). Therefore I have rewritten the lead as an attempt to clarify the various meaning of the subject of the article. IMHO, the remainder of the article must be rewritten in the same line. Also the long term discussion about merging or not with constant could be solved rather easily with this approach: A constant is either a fixed object (mathematical constant) whose name may be an alphabetical character (1 and π are constants) or a variable that is considered as fixed in some context.

I apologize that the second paragraph may be too technical for some readers. But, it must be kept for the readers that need a definition that is more accurate than the previous one.

D.Lazard (talk) 16:04, 12 November 2013 (UTC)

Remember that the lead should introduce the topic and give an overview of the article. Have you considered writing a section "Definition" that gives an accurate, modern definition? For the typical reader of such an article it is probably not very helpful to start discussing functions, arguments, and values in the lead paragraph. Also, the reference from the Syracuse university is no longer cited as far as I can see. Isheden (talk) 08:45, 13 November 2013 (UTC)

Except in mathematical logic, I do not know any proper definition (i.e. mathematical definition) of the concept of variable. Even in mathematical logic, there are several definitions, as I have pointed out in the lead, and there would be inaccessible for almost every reader. Therefore I do not see what could be put in a section "Definition". On the other hand the lead must introduce the topic for all the readers. Thus, as "variable" has several different but strongly related meanings, they must be disambiguated in the lead. About the mention of arguments and values of functions, it is needed in the lead because the idea that a variables is something that varies, and the word itself, take their origin in the historical elaboration of the concept of function. This dynamic interpretation is yet strongly used in elementary curses and, at higher level, in informal reasoning. The fact that a variable may varies is not used in formal description nor in proofs. This apparent contradiction is highly confusing for readers with a low mathematical level and deserve therefore to be clarified in the lead. To clarify that in a few words, I do not see a better way than giving the prototypical example.

I'm not convinced that a complete rewrite of the lead is the way forward at this point. Normally the article body should be reworked first and then the lead may be adjusted to reflect the changes in the article body. I also think that discussions of limits and notation such as "for all" and "it exists" cannot be considered an informal introduction to variables (as per WP:MOSMATH) and therefore should be kept out of the lead. The lead should rather clarify the context-dependent distinction between variables and constants. At present, constants are hardly mentioned at all. And I don't see the need for disambiguation of variables in computer science, since the mathematics disambiguation is in the article title. Isheden (talk) 11:31, 13 November 2013 (UTC)

I agree that, normally, the lead must summary the content of the article. But this rule, clearly, does not apply to stubs, and, presently the article is a stub, even it is not tagged as such. I will explain below why it is a stub, and what remains to do for having an acceptable article. Nevertheless, I agree that some content of the lead may (and must) be moved in the article body, when the content will be sufficiently expanded.

Before describing what is lacking in the article, we must examine the present content to see why it is a stub, despite its length.

• Section "Dependent and independent variables": This section gives an undue weight to a terminology which is dangerous to use and is rarely used in modern mathematics (mathematical analysis, theory of differential equations, ...)
• Section "What it means for a variable to vary": This section and its title are WP:original research. Moreover it contains many assertions that are disputable or wrong. Firstly the assertion that variability is an essential property of variables. Also the suggestion that unknowns, parameters and indeterminates are not variables. And the last paragraph of subsection "Examples" is definitively wrong. Thus this section must be replaced by something completely different.
• Sections "Notation" and "Naming conventions": These sections have essentially the same subject and deserve to be merged and shortened. Also the "naming conventions" are not conventions but simply common usage.
• Section "Applied Statistic": It is out of scope of this article. It could be relevant here only if a similar section of the article would be devoted to many other areas of mathematics. Note that this section does not use the word "random variable", even if it is strongly related to the subject. Also, what is the difference between "statistic" and "applied statistic"? As far as I know, statistic is always applied, and may be considered as "applied probability".

Therefore, after removing what deserves to be removed, the body of the article consists in a single section "Notation" and a section "Dependent and independent variables", which needs to be completely rewritten. Now the lacking sections.

• Genesis and evolution of the notion of variable. Such a section is essential for a topic that is not mathematically defined and, therefore, may be and is interpreted differently by different people.
• Specific kinds of variables. Such a section could be introduced by something like: In most mathematical formulas, many variables may occur, that play different roles. Therefore, some names or qualifiers have been introduced to distinguish them. This section needs text or subsections for quantified and free variables, parameters, unknowns, indeterminates, dependent and independent variables, bound and unbound variable (maybe in a section "Variable in computer science"), random variable (probably in a separate section), ...
• Variable in mathematical logic
• Variable in computer science

This list is probably incomplete, please, add what I have forgot.D.Lazard (talk) 14:26, 14 November 2013 (UTC)

I'm critical of the way the article is developing. The new lead is too formal and hard to understand for anyone who is not already versed in calculus. Giving the argument and value of a function as examples of variables is misleading, because argument often refers to a specific input to the function, whereas value refers to the specific output for that input. And a reader interested in what a variable is can hardly be expected to understand the specific meanings of function, argument, and value in mathematics anyway. Regarding the article body, one of the main topics in my view should be to discuss variables in probability theory and statistics, including continuous and discrete random variables, predictor (independent) vs. response (dependent) variables in statistical models... That whole section has now been deleted from the article. An article about variables in mathematics cannot focus only on calculus. Isheden (talk) 20:16, 17 November 2013 (UTC)

I do not believe that someone who has never seen the notation y = f(x) can really understand what is a variable. In any case, as the word itself takes its origin in infinitesimal calculus, a reference to calculus is needed for explaining the etymology and avoiding the wrong interpretation that "a variable is something that varies". Nevertheless, I have split the first paragraph into "elementary mathematics" and "calculus" and expanded the first paragraph. D.Lazard (talk) 14:13, 20 November 2013 (UTC)

You write that variables in applied statistics is out of scope of this article. I just wanted to point out that Variable (statistics) redirects to this article. If there is consensus that variables in statistics should not be covered here then we need a separate article about that. There are several types of variables that should be described there: [1][2] Isheden (talk) 11:51, 18 November 2013 (UTC)

As far as I can understand the notion of variable in statistics is closer to variable (computer science) than to variable (mathematics): it is a variable (computer science) attached to each entry in a data base, or, in mathematical terms, a function having the entries of a data basis as domain. In any case the statistics terminology is very specific and is not really useful for readers that are not primarily interested by statistics. Any terminology that is specific to statistics must be defined in an article about statistics not here. When a understandable definition of variable (statistics), would appear somewhere in Wikipedia, some text will need to be added here to explain how it is related to, and how it differs from variable (mathematics). Nevertheless, the text that I have removed (it may be retrieved from the history of the article) may be used as the basis of a stub-article "variable (statistics)". This was recommended in a previous discussion at talk:variable. D.Lazard (talk) 18:03, 19 November 2013 (UTC)

If such an article is created, how about merging it with dependent and independent variables? That article also needs a substantial rewrite. Isheden (talk) 12:06, 18 November 2013 (UTC)

Note also that there is a separate article Variable (computer science) with a disambiguation link from Variable. Isheden (talk) 11:55, 18 November 2013 (UTC)

I did know that. Probably a hatnote is needed. Nevertheless, a section Variable in computer science is needed for explaining the strong relationship between the two notions (with a {{main|Variable (computer science)}} hatnote) D.Lazard (talk) 12:09, 19 November 2013 (UTC)

There used to be an article (see Talk:Variable) for the various related notions. Perhaps splitting it was not such a good idea based on WP:CONCEPTDAB? Isheden (talk) 12:53, 19 November 2013 (UTC)

Variables versus parameters

Having read some of the above discussions, I can see that it is a difficult issue trying to juggle both the narrow concept of "variable" (it must vary within the given context) and the broad concept (including the letters representing parameters). I disagree with this article's unsourced current treatment of parameters of equations as "variables". From the article's lead:

A typical example is the quadratic formula, which allows to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation to the variables that represent them. ["The variables that represent them" refers to the letters representing parameters.]

And from the beginning of the section "Specific kinds of variables":

For example, in the general cubic equation

$ax^{3}+bx^{2}+cx+d=0,$

there are five variables.

In my experience, in this context only the unknowns are called variables. As a quick source, this is confirmed by Mathworld, "Variable":

In a polynomial, the variables correspond to the base symbols themselves stripped of coefficients and any powers or products.

The variables in a polynomial can be extracted using the Mathematica command Variables[poly].

Arguments that are typically varied when plotting, performing mathematical operations, etc., are termed "variables," while those that are not explicitly varied in situations of interest are termed "parameters."

While undoubtedly in other contexts "variable" is used more broadly, in this context it is used as a synonym for "unknown". I think this should be changed in this article. 208.50.124.65 (talk) 21:23, 14 July 2014 (UTC)

This usage of " variable" as "unknown" also appears in our articles polynomial, algebraic equation, linear equation, and conic section#Cartesian coordinates. Of course Wikipedia does not consider itself to be a reliable source, but this illustrates how math writers here use the term. I can't find any counterexamples. 208.50.124.65 (talk) 21:56, 14 July 2014 (UTC)

And if $ax^{3}+bx^{2}+cx+d=0$ really had five variables, we would call it a multivariate equation, which we don't. Any objections to my correcting the above-quoted passages? 208.50.124.65 (talk) 16:07, 15 July 2014 (UTC)

Our article Parameter explains it well: in the context of y =ax² , changing the parameter a gives a different (though related) problem, whereas the variations of the variables x and y (and their interrelation) are part of the problem itself. Hearing no objection, I'll correct the present article. 208.50.124.65 (talk) 20:49, 15 July 2014 (UTC)

I do not agree. In modern mathematics the distinction between "variable", "parameter" (and also "unknown", ...) is only a question of context. In other words, a variable is a symbol, usually a letter, that represent some quantity. Moreover your edits make the section contradictory withe the lead. Therefore, I'll revert your edit as confusing and disputed. Please reinsert it only if a consensus appears in this talk page. D.Lazard (talk) 13:44, 16 July 2014 (UTC)

Sources trump your claim. You reverted my sourced edit to an unsourced set of assertions. Go to the library and randomly select a math book, and see if it says that

$ax^{3}+bx^{2}+cx+d=0$

has 5 variables in it. Find a discussion of multivariate polynomial equations and see if this equation counts as one of them. Do you really believe that this equation is multivariate?!

Yes, the difference between parameter and unknown is context-specific. In the context of polynomial equations, a,b, etc. are not called variables, at least not in English. Please provide sources for your assertions that in the quadratic equation of the lead, and in the subsequent cubic example, a, b, c, d are called variables, and in the absence of sources to that effect, please restore my reversions of those claims. 208.50.124.65 (talk) 22:20, 16 July 2014 (UTC)

For that matter, see your own edit of last November here

[3]

in which you state that in the quadratic, a, b, c are parameters and you let stand the statement that x is the variable and by implication the only variable. 208.50.124.65 (talk) 22:34, 16 July 2014 (UTC)

Variable and value

In the article text there is "the notation y = f(x) for a function f, its variable x and its value y".

This looks wrong since y is a variable too not a value. y only refers to a particular value when x is given a particular value.

Similarly at the top the article has "The concept of variable is also fundamental in calculus. Typically, a function y = f(x) involves two variables, its argument x and its value y."

A value could be a number for example, which of course is not a variable. 88.203.90.14 (talk) 21:39, 2 August 2014 (UTC)

IMO, the article was correct. The problem that you quote is only an insufficient distinction between the name, the variable, and the named object, the value of the variable. I have edited the lead for a better distinction. D.Lazard (talk) 08:10, 3 August 2014 (UTC)

External links modified

Hello fellow Wikipedians,

I have just modified one external link on Variable (mathematics). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20140116020503/http://cstl.syr.edu/fipse/algebra/part4/append1.htm to http://cstl.syr.edu/fipse/algebra/unit1/..%5Cpart4%5Cappend1.htm

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 18 January 2022).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 14:52, 2 August 2017 (UTC)

Old discussion

See the discussion page Talk:Variable for the common discussion history of Variable (mathematics) and Variable (programming). prohlep (talk) 15:49, 3 October 2009 (UTC)

---

TO WIKIPEDIA EDITORS :

do you computer programmers realize argument is not what it is called?VARIABLE the SYMBOL it is a CONSTITUENT A MODIFIER OF THE ARITY THE ASPECT THE DEGREE OF THE VALUE THE VALUE THE NATURAL NUMBER IS THE ARGUMENT AND THE VARIABLE IS THE CONSTITUENT NOT AN ARGUMENT THE CONSTITUENT VARIABLE IS A RANK ORDINAL NUMBER ARITY ASPECT OF VARYING DEGREE OF THE VALUE ITS NATURAL NUMBER THE ARGUMENT THE VARIABLE IS A MODIFIER A CONSTITUENT NOT ARGUMENT SO 3 x where 3 is the VALUE THE NATURAL NUMBER and x the symbol the variable its constituent modifier to the argument the value of three so the symbol variable aspect the degree of or number of how many are in the value is the constituent so 3 is value of ther natural number, 3 x, if x is 2 and 3 multiplied by 2 = 6 then x=2 so x is the constituent modifier how many are in the value of it so the power of x is 2 so the variable degree of how many 3's there are is 2 3's =6 so 3 + 3 = 6 or 3x, or 3 to the power of 2, 3 multiplied by 2 = 6 — Preceding unsigned comment added by 209.240.125.195 (talk) 00:32, 28 February 2018 (UTC)

"Pronumeral" listed at Redirects for discussion

A discussion is taking place to address the redirect Pronumeral. The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 January 13#Pronumeral until a consensus is reached, and readers of this page are welcome to contribute to the discussion. D.Lazard (talk) 17:52, 13 January 2021 (UTC)