Talk:Variable (mathematics)

"A variable is a symbol"

The sentence "A variable is a symbol" is blatantly wrong, and I added a reference to confirm this. Just to give one out of many possible examples, the distance from the Earth to the Sun is a variable. It was a variable before mankind existed, and started to denote this variable by symbols. Suppose a particular human decides to denote this quantity by r_E, that doesn't suddenly create a new variable. The variable is still the same.----Ehrenkater (talk) 10:49, 5 October 2018 (UTC)

This article is about variables in mathematics, not about the common meaning of "variable", which is an adjective and not a noun, as it is in mathematics. It is wrong that "the distance from the Earth to the Sun is a variable". The truth is "the distance from the Earth to the Sun is variable, and may be represented, in formulas, by a symbol called a variable". Also, we must take into account that, in modern mathematics, the noun "variable" is widely used for symbols representing quantities that cannot vary. For example, in an equation, such as the quadratic equation, the unknown is generally represented by the variable x; this variable can have up to two values, which cannot vary. D.Lazard (talk) 13:36, 5 October 2018 (UTC)

E and Pi are not variables

I found e and π in the list of variables. But they're not variables because they have known values (e ≈ 2.78, π ≈ 3.14). so, why are they here? 2600:8800:5112:7500:B09F:C337:A2AB:2DA0 (talk) 03:48, 11 January 2022 (UTC)

It is said in the introduction that a variable may represent any mathematical object. Therefore, it may represent also a constant. I have edited § Specific kinds of variables for clarifying this. D.Lazard (talk) 10:50, 11 January 2022 (UTC)

it may be true, but if it's really true, then I may or may not think that π and e are not approximately 3.14 and 2.78. 2600:8800:5112:7500:F9EE:B252:FD43:30FC (talk) 07:30, 14 January 2022 (UTC)

Correct. You may find other uses of $\pi$ and e in projection (mathematics)#Definition and Quintic function. D.Lazard (talk) 09:18, 14 January 2022 (UTC)

Changes in the lead

An editor is starting an WP:edit war for changing the lead. Here are some reasons of the revert.

• The change of the order of the paragraphs makes the lead confusing, since in the new version, "This is in contrast to ..." refers grammatically to the sentence on mathematical logic.
• There is a WP:SUBMARINE link to domain of discourse, which is a philosophical concept not used in modern mathematics.
• The source is more 100 years old and the edit does not take into account that mathemaical logic has dramatically evolved since Russel's time.
• Changing "a mathematical object" into "an arbitrary object in some specified domain" is a clear disimprovement: a variable may represent a matrix, which is clearly a mathematical object, but one can define A as a variable representing a matrix without specifying the domain set (called "domain" in the edit) to which the represented matrix belong.

These reasons explain why I'll reverting again this edit. D.Lazard (talk) 14:37, 23 August 2024 (UTC)

I agree with your comments, D.Lazard. There are also other problems with the editing you refer to; for example "Some authors also consider more abstract objects to be constants, for instance and [sic] the identity element of a group" misses the point: since a group has only one identity element, if I use a symbol meaning precisely that one element and no other then that symbol is a constant, just as much as a symbol used to represent precisely one number is a constant, or a symbol to represent precisely one object of any other kind. Any author who doesn't "consider" that to be so would, it seems to me, be using the word "constant" in a very unorthodox sense; or have I misunderstood? JBW (talk) 21:50, 25 August 2024 (UTC)

That's a fair objection. But the meaning of "an identity element of a group" is meant more abstractly, not as any specific construction of a group.

For instance, take the groups (1) addition over the integers, and (2) multiplication over the integer powers of 2. These two groups are isomorphic, so I might define the group that describes them both. Here, the identity element can technically denote either 0 or 1, depending on the construction but some may consider in the abstracted group in isolation that the identity element is itself a constant. In the same way that 0 and 1 themselves do not denote any particular construction of 0 or 1 objects. Farkle Griffen (talk) 22:51, 25 August 2024 (UTC)

The edit has been made in accordance with what you say here. Specifically,

• no paragraphs have been moved
• no link to “domain of discourse” has been added
• modern sources are used
• only a small piece of the definition was changed to clarify the topic

The reason for the edit: One should make clear the difference between variables, constants, and general symbols in mathematics. Referring to constants as a kind of variable is confusing for most readers and not how most people use those terms.

A note on the domain of discourse article: it should be noted that it is listed as a mathematics article; it is introduced as “In the formal sciences” which mathematics is a part of, and links to the articles related in mathematics (such as Universe set); and uses mathematical examples to describe the topic. So it really shouldn’t be written off so quickly as “a philosophical concept not used in modern mathematics.” In regard to your example, you have exactly specified the domain set; that is the set of matrices. Farkle Griffen (talk) 22:37, 25 August 2024 (UTC)

@Farkle Griffen: I agree with your comment that "Referring to constants as a kind of variable is confusing for most readers and not how most people use those terms." I have previously expressed my disliking of referring to them in this way. As for "the domain of discourse", I partially agree with your comments, but the expression is not currently in common use in mathematics (in fact I'm not aware that it is currently in use in mathematics at all), and also the article goes into the topic in ways which are not really relevant to the content of the article on variables; for both of those reasons I don't think that linking to it is likely to be helpful to most readers. JBW (talk) 14:58, 26 August 2024 (UTC)

I agree the link could be better, but Wikipedia doesn't seem to have an article about the domain/range of a variable in mathematics, and that was the closest article I could find. Linking to domain of a function would be even more confusing. It's possible that one could be created, but I don't think that's necessary.

In many of the sources I've recently found (which user: D.Lazard appears to have removed), they often use the term range of a variable, rather than domain, to refer to the set of constants it can represent. I think a sentence could be added to introduce this term. Farkle Griffen (talk) 15:16, 26 August 2024 (UTC)

D.Lazard's revisions

User D.Lazard continues to revert the article to a version that is not supported by any sources, and contradicts all sources that define the term. Enforcing the definition "a symbol that represents a mathematical object", and asserting that constant symbols are variables.

Source 1) "A variable a symbol representing an unspecified element of a given set"

Source 2) "A variable is a symbol that holds a place for constants."

Source 3) "We use the term variable in keeping with the usage of Collis (1975), Küchemann (1978), and a number of other researchers, such as Philipp (1992), who terms it a varying quantity. When a letter is used as a variable, the letter is seen as representing a range of unspecified values, and a systematic relationship is seen to exist between two such sets of values” (Küchemann 1981, p. 104)."

This author distinguishes between variables and placeholders, using them to mean what this article calls free variables and bound variables respectively.

They define placeholders as "We use the word placeholder to mean a letter standing for a number that will be provided in a particular problem or context. A placeholder is often called a given or a constant; in specific instances it is a parameter or a coefficient. Like a variable, a placeholder is indeterminate, but whereas a variable can stand for an entire set of values, here the point is that the equation or expression really stands for an entire set of equations or expressions. For instance, in the equation “ax² + bx + c = 0,” a, b, and c are placeholders (in particular, coefficients). This equation in fact stands for an entire set of quadratic equations (if a≠0), and it is understood that in a specific context these letters will be replaced with specific numbers"

To D.Lazard's edit summary: "The removed paragraph does not says that constant are variables, but the letters that denote them are variables."

None of the sources say that a variable is simply a symbol. All of them are very clear a variable has the property of being, at the moment, unspecified. Constant symbols are not usually considered "unspecified". While, as he has noted, the symbols for pi and e have been used as variables, this does not mean that they are always used as variables, it is just that some contexts use the symbol as a variable, while others use it to denote a particular constant. Constants and constant symbols are not variables, and this should be made very clear. Farkle Griffen (talk) 12:27, 28 August 2024 (UTC)

@D.Lazard, please do not edit war. I am trying to engage with you outside of the article space, but you have not responded. Farkle Griffen (talk) 18:30, 28 August 2024 (UTC)

@D.Lazard, I have added four more sources, totaling 7 sources which very clearly state that a variable represents an unspecified constant. None of which support "variable" denoting a particular constant. Do you have any sources supporting this definition? Farkle Griffen (talk) 06:05, 1 September 2024 (UTC)

@D.Lazard, Have you considered that the term may be used diffrently in English versus French? Farkle Griffen (talk) 16:57, 1 September 2024 (UTC)

@D.Lazard, I have found a source, ISO 80000-2: https://www.iso.org/standard/64973.html, which explicity notes e, pi, and i as not variables. It is for this reason I will editing the article to be more inline with the sources. Farkle Griffen (talk) 04:33, 5 September 2024 (UTC)

ISO is not a reliable source for mathematics. In particular it promotes roman fonts for the mathematical constants e and i, while in Mathematics and Wikipidia, the common convention is italics (see MOS:MATH#Roman versus italic). Also, for saying that e and i are or are not variables, you must be clear whether you are talking of the symbol or the number. D.Lazard (talk) 08:23, 5 September 2024 (UTC)

Thank you for responding.

While you may disagree about the validity of the source, you have not provided a single source. While other conventions exist, the purpose of that source is not about the italicization, but rather it is a source which explicitly notes that the symbols e, pi, and i, when denoting constants, are not considered variables.

I have asked you to provide a source, I have provided 7 sources (now 8), I have left two talkback requests on your talk page, and all of my edits have been in accordance with your previous discussion. If you revert my edit again without supplying even a single source, or responding to each of my sources showing how, (as you continue to say in your edit summaries) "I am misinterpreting them", I will be reporting this as WP:Edit warring behavior.

If you disagree with what I have written, you are free to edit it. However, you should not imply that the symbols denoting constants or constants themselves are variables without doing one of the options mentioned above.

Thank you. Farkle Griffen (talk) 13:43, 5 September 2024 (UTC)

On the description of "unknown"

The article currently seems to describe the unknown of an equation as a kind of bound variable, but this interpretation is not always true. For instance, one may regard the unknowns in an equation to be free variables, we call the "solutions" the values of the variables that make the equation true, and "Solving an equation" refers to finding an equivielnt formula that makes the solutions more obvious. For instance, the formula $x^{2}-3x+2=0\iff (x=1{\text{ or }}x=2)$ is a tautology.

I'm not too upset if the current description doesn't change though, it is just something I'd like to note. Farkle Griffen (talk) 17:26, 28 August 2024 (UTC)

The unknowns of an equations are variables such that the value is unknown before solving. Solving an equation is not to find an equivalent formula; it is to find the value(s) of the variable that satisfy the equation. Also the above equivalence is not a tautology; it is a theorem whose proof is a very simple computation in one direction, but is less obvious in the other direction (for proving that there are no more solutions). D.Lazard (talk) 17:38, 28 August 2024 (UTC)

A tautology is a formula which is always true. If you plug in any real number for x, that formula will be true. Needing a proof does not mean it's not a tautology.

"Solving an equation is not to find an equivalent formula; it is to find the value(s) of the variable that satisfy the equation."

These two statemnets are not necessarily disctinct. One just needs specify the form the formula must be in to consider the equation "solved". Farkle Griffen (talk) 17:54, 28 August 2024 (UTC)

We are talking of elementary mathematics and not of formal logic. "Tautology" is a term that is not used in mathematics, except in mathematical logic. So I understood the term as in tautology (language). Even if one use the sense of tautology (logic), your example is not a tautology, since the formula becomes false if x interpreted as a square matrix. D.Lazard (talk) 09:29, 29 August 2024 (UTC)

I am talking in terms of mathematical logic. "Free and bound variables" is not common terminology outside of mathematical logic.

And you're kinda missing the point here. This conversation isn't meant to be about the definition of "tautology". My point is that it doesn't make much sense to define unknowns as a kind of bound variable.

Nevertheless, I have found a source that specifies exactly what I'm saying here... [R. Wolf] A Tour Through Mathematical Logic, p.17, specifies that in basic algebra, the unknowns in an equation are free. Farkle Griffen (talk) 20:22, 8 September 2024 (UTC)

The term "bound variable" is not presented in the article as being related to the unknown of an equation, and nobody but you use this term in the context of equation solving. D.Lazard (talk) 19:56, 9 September 2024 (UTC)

Edit revert

@D.Lazard: re [1]. "Variable (mathematics)" is not ambiguous. "Mathematics" is not "computer science". No other use at disambiguation page Variable refers to mathematics. The hatnote is not helpful, and is not required per WP:NAMB. Please further explain. Shhhnotsoloud (talk) 15:32, 11 November 2024 (UTC)

Maybe the distinction between these two concepts is clear to you, but certainly not for most readers. This is why a hatnote is useful. However the template {{distinguish}} is more adequate in this case, and I have changed the hatnote for using it. D.Lazard (talk) 16:05, 11 November 2024 (UTC)