This is the
talk page for discussing improvements to the
Order of operations article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Archives:
1,
2,
3,
4Auto-archiving period: 365 days
![]() |
![]() | This ![]() It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||
|
There is a current version of this article that insists that a parenthesis is a mathematical operation and that PEDMAS is a law of mathematics. A parenthesis is a symbol of grouping and PEDMAS is a mnemonic. No reference is given suggesting otherwise. The person who wants this in the article has restored this claim after my revert with the comment "Take it to the talk page." I would appreciate the opinion of others. Rick Norwood ( talk) 19:21, 10 April 2023 (UTC)
1. Parentheses: any operation or series of operations delimited by parentheses or other symbols of grouping (the order of operations applies also to such grouped operations). This resolves another issue of the current version, namely that it is not said that the order of operations applies also inside parentheses. D.Lazard ( talk) 18:32, 12 April 2023 (UTC)
this once was taught in grade 1 ... back in the 60's– this was never taught in the first grade. More like 5th–7th grade. It definitely does not date to Thales or Euclid; modern mathematical notation largely arose in the 17th–19th century, and was initially not very settled. The teaching of formal 'order of operations' rules comes from the 19th century.
parenthesis are ( ) ... { } are NOT parenthesis– in this context the word "parentheses" covers all kinds of grouping punctuation. Often these are ordered from inside out as: round "parentheses" (), square brackets [], curly braces {}, and later sometimes angle brackets etc. However, in technical literature it is also common to just use nested parentheses, reserving other kinds of brackets for other purposes such as real intervals, set-builder notation, bra-ket notation, matrices, the Iverson bracket, and so on. – jacobolus (t) 01:48, 17 February 2024 (UTC)
I still think parentheses are a separate topic, which are not clearly explained by an instruction to "do them" first. You don't "do" parentheses. But there is another comment above that I'm curious about: "the term more commonly used in the rest of the English-speaking world". What term is that?
In the US, we talk about (parentheses), [brackets], and {braces} all of which are sometimes used as symbols of grouping and all of which have other uses. Parentheses are used both for points (a,b) and for open intervals (a,b) and there is no way to tell which use is intended except from context. Brackets are use for closed intervals [a,b]. Braces are use for sets {a,b} and an open brace is used for a system of simultaneous equations. (Parenthetic aside, off topic: My students are no longer taught much vocabulary in the US K-12 system, so I now have to say, instead of "brackets", "square brackets" and instead of "braces", "curly braces", for my students to know what I'm talking about.
Wikipedia should have an article titled "Symbols of grouping". I'll think about creating one. Rick Norwood ( talk) 10:41, 14 April 2023 (UTC)
I recently added a section "In popular culture" discussing internet memes with ambiguous mathematical expressions. It was reverted because "it was already covered" elsewhere. But the current coverage is buried in the middle of a subsection, doesn't provide much coverage, and cites a source that is self-published.
I don't have any stats to back this up, but my sense is that a large amount of traffic to this page is driven by these internet memes. Since our job is to serve our audience we should provide a more prominent treatment of ambiguous expressions.
I hope that the other editors will consider the since reverted section and think about how to incorporate it into the article. Mr. Swordfish ( talk) 15:56, 6 July 2023 (UTC)
Apologies in advance for being a nudge here, but I'm now wondering whether those ambiguous mathematical expressions so often posted on social media are actually memes. I used that term here on the talk page as a kind of shorthand, but did not use it in my proposed edit ( https://en.wikipedia.org/?title=Order_of_operations&oldid=1163541119#In_popular_culture).
So, are they memes? If so, then clearly they are internet memes and we can call them that. But after reading the definition of meme, I'm not convinced they are, and putting my wikipedia editor hat on, we'd need some source saying that these things are in fact memes regardless of whatever conclusion I might draw from the definitions.
So, anybody got a cite that calls these things "memes"? If not, we should change the language. Mr. Swordfish ( talk) 23:03, 9 July 2023 (UTC)
Why do we use this phrase in the Definition section?
I've looked at every single source cited in the article, and except for the non-US sources that use "Brackets" and the Wolfram cite that uses "Parenthesization" every single cite simply uses the word "Parentheses". And the Wolfram cite links their word to their article on "Parentheses.
So, what's up with us making up our own nomenclature? If there's reliable source using the phrase "Parenthetic subexpressions" we need to cite it. Otherwise, it seems fairly clear to just repeat the language that all the cited sources use. Other opinions? Mr. Swordfish ( talk) 00:04, 18 August 2023 (UTC)
At one point, I spent a substantial amount of time rewriting this article to make it mathematically accurate. Other editors immediately reverted my rewrite and reinserted incorrect information, apparently on the grounds that it was what they were taught in grade school.
I would really like not to have to continue teaching my college classes that the things they were taught in grade school are wrong, and I think good Wikipedia articles would be a step in the right direction, since most of my students use Wikipedia. But the fans of parentheses as operations rather than symbols of grouping will, as can be seen above, argue illogically and interminably.
Will anyone who actually knows something about logic and mathematics help? Or should I give up and move on to another article? Rick Norwood ( talk) 10:54, 21 August 2023 (UTC)
That would probably be an improvement, but the correct statement is this: if there is an operator both to the left and to the right of a given expression, the operator higher on the list should be applied first. If both operators are on the same level, the associative law applies, and applying either first gives the same results. The main point that it is perfectly all right to add two numbers somewhere in an expression before you perform a multiplication somewhere else entirely.
I'm going to make a change, and we'll see what happens next. Rick Norwood ( talk) 10:30, 22 August 2023 (UTC)
Ah, well. It takes a long time to do a carefully rewrite, and only seconds to revert it. Apparently, even though we all agree that parentheses are not an operation, there are enough people who want this article to say that that it keeps going back in. This time I am going to do just one thing, remove the claim that parentheses are an operation. We'll see what happens next. Rick Norwood ( talk) 19:07, 22 August 2023 (UTC)
My previous edit stood for more than an hour, so I'm going to start moving the material in this article that says nothing about the order of operations to the article titled symbols of grouping. Rick Norwood ( talk) 21:16, 22 August 2023 (UTC)
I've added references. If reverted again, I'll add another reference and restore what makes sense.
Mr. Swordfish argues that, since this is an elementary article we do not need to limit "operation" to the mathematical meaning. We can use the dictionary meaning. But the title of the article uses "operations" in the mathematical meaning, not the dictionary meaning, and so the article should do the same.
Mr. Swordfish and several others share a consensus that there is a difference between a mathematical operation and a symbol of grouping. Why, then, does he keep adding Parentheses to the list of mathematical operations? What does he think that adds to the article? Rick Norwood ( talk) 21:55, 22 August 2023 (UTC)
On the contrary. No reliable mathematical source says parentheses are operations. You are the only person who says this.
It is true that essentially all US grade school textbooks list parentheses in their order of operations. They also have many other mistakes, such as forcing students to add from left to right. The people in power, who decide the grade school curriculum, want things the way they have always been. But Wikipedia uses professional terminology, not grade school terminology. Why do you want Wikipedia to repeat grade school mistakes? Rick Norwood ( talk) 23:05, 22 August 2023 (UTC)
I've added another reference. The Common Core does not include PEDMAS. Teachers teach PEDMAS because they teach what they were taught and books include PEDMAS because teachers like it. But it is not in the Common Core and the fact that it is wrong has been pointed out many times.
I'm surprised to find D. Lazard on the other side of this question, since he is an editor I respect. I can only suggest he Google "is pedmas correct" or "is pedmas still in common core".
As for the article not saying Parentheses are operations, read the section carefully. Here is what it says:
"The order of operations, that is, the order in which the operations in a formula must be performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as:[1][5][6]
Parentheses Exponentiation Multiplication and Division Addition and Subtraction"
Clearly, the implication is that the summarized list is a list of operations.
But the main point is that the Common Core has abandoned PEDMAS, that many sources say clearly that PEDMAS is wrong, and there is no good reason to perpetuate this error. Rick Norwood ( talk) 12:30, 23 August 2023 (UTC)
This means that to evaluate an expression, one first evaluates any sub-expression inside parentheses, working inside to outside if there is more than one set.Also, an initialism, such as PEDMAS cannot be wrong by itself; the problem with it is that it can be misleading if interpreted as a list of operations (what it is not). In any case, as PEDMAS is not mentioned in the current version before section § Mnemonics, you cannnot use your opinion on PEDMAS to force modifications of sections that do not mention PEDMAS at all. D.Lazard ( talk) 13:01, 23 August 2023 (UTC)
Clearly, you have made up your mind. I wish you would at least took at the references, and the other changes you reverted, which moved discussions of symbols of grouping. As things stand, unless someone else supports the view I support, which is the view of the Common Core document, then this article will continue to mislead readers.
Yes, a consensus is important. But in Wikipedia, authoritative references are even more important. And I am pretty sure that no mathematical publication, as distinct from a grade school publication, has the list with parentheses at the top. Rick Norwood ( talk) 13:20, 23 August 2023 (UTC)
The order of evaluation, that is, ..." (change suggestion underlined). I believe to remember that recently I made such an edit, but apparently it got reverted somehow. - d Jochen Burghardt ( talk) 18:20, 23 August 2023 (UTC)
We have solid sourcing that PEMDAS is used in the US and France, and also that BEDMAS is used in Canada and the UK.
We don't have sourcing for the geographical distribution of BODMAS or BIDMAS, so I propose simply writing around the gap instead of making specific claims that are not supported by cites.
Also, the "O" in BODMAS is sometimes said to stand for "Order" (an archaic word for exponentiation), "Of" [a], in addition to the Operations that we state in the text. Seems like we should include those alternatives.
Per the above, I suggest the following text for the third bullet point:
New references are bare urls for now - we can format them in a better manner if this change is accepted. Mr. Swordfish ( talk) 14:31, 23 August 2023 (UTC)
I'll only point out (again) that the Common Core standards do not use PEMDAS. I suppose it needs to be here, since most US grade schools ignore the Common Core standards, even when their state requires them. I agree with Mr. Swordfish about shortening this section. Rick Norwood ( talk) 10:24, 24 August 2023 (UTC)
References
Syllabus_2019
was invoked but never defined (see the
help page).Vedantu_2019
was invoked but never defined (see the
help page).The article uses the term "precedence" without defining it. There are almost 20 incoming redirects that have "precedence" in their title, and many others that use the pipe [[Order of operations|precedence]]. In particular, it is almost impossible for a beginner to know which of addition and multiplication has the higest precedence.
So, a definition of precedence must be given in the lead, and this must be expanded in a specific section. Someone is willing to do that? D.Lazard ( talk) 16:42, 23 August 2023 (UTC)
Again, I agree with Mr. Swordfish. There is a Simple English Wikipedia for people who do not know the meaning of common words such as "precedence". Rick Norwood ( talk) 10:28, 24 August 2023 (UTC)
This is getting really strange. Mr. Swordfish says that in this article it is ok to use the dictionary meaning of operation, which has a special mathematical meaning. D. Lazard says it is not ok to use the common word precedence, which means "which comes first", and is not used here to mean anything else but "which comes first". Rick Norwood ( talk) 10:06, 25 August 2023 (UTC)
References
The opening sentence of the Programming languages section states:
and while this is correct, it could be misleading. My experience is that nearly every programming language uses the "standard" operator precedence (with the usual caveats above) so stating it as "Some" implies that it is not the norm, or even a majority.
Looking at this list of most popular programming languages the only exceptions that jump out as exceptions are Lisp and Haskell, which are pretty far down on the list, and html which doesn't really do math at all. Perhaps there are others since I'm not familiar with all of them, but all the more common ones use the standard operator precedence (to the extent that there is one - i.e. grouping symbols, exponents, multiplication/division, and addition/subtraction in that order; beyond that all bets are off)
I don't think it would be original research to look at that list and say "Most commonly used programming languages..." instead of "Some programming languages..." but some may argue that point. Other suggestions for how to word this to avoid possible mis-representation? Or a good cite for this change? Mr. Swordfish ( talk) 13:50, 30 August 2023 (UTC)
The second sentence of this article is:
This is certainly correct, but might be too much this early in the article. My sense is that most of our readers are not familiar with the concepts of functional or polish notation, and those systems are not what this article is about. Granted, there are links for the reader to click, but my reading (assuming the perspective of a non-mathematician) is that this sentence is a distraction from the main thrust of the article.
I'd suggest simply moving this sentence to later in the article, perhaps just a paragraph or two. Alternatively, provide a parenthetical example so the reader doesn't have to click on the link to find out that infix notation is just the familiar way of writing mathematical expressions that they have come to know and love:
Other opinions? Mr. Swordfish ( talk) 15:28, 2 September 2023 (UTC)
when infix notation is used" to "
when the usual notation (called infix notation) is used". Adding an example for infix isn't useful, except when it is contrasted with (e.g.) Polish notation; so we could possible add a sentence like "
For example, the infix expressions 3 × 4 + 5 and 3 × (4 + 5) are written as + × 3 4 5 and × 3 + 4 5 in Polish notation, respectively.". I'm afraid, however, that such a sentence won't be understood without additional (and then distracting) explanations. Maybe, reverse Polish notation is easier to explain; in fact is has been employed by HP calculators, so it may be known better. - Jochen Burghardt ( talk) 15:54, 2 September 2023 (UTC)
I am not surprised that my removing the false information "operations with the same precedence are generally performed left to right" was reverted. So many people have been taught that false "rule" in grade school that many people insist that what they learned in grade school is true. But all mathematicians know that addition is commutative and associative and multiplication is commutative and associative, and mathematicians generally perform operations in whatever order is most convenient.
It is a bit ironic that I think 12/6*2 = 4, which is what you get when you perform operations left to right. But most physicists insist that 12/6*2 = 1. Of course, my reasoning has nothing to do with left to right. It makes sense to me that subtraction is addition of the opposite and division is multiplication by the reciprocal. It is strange that after all these centuries, there is nobody who can settle the question. Rick Norwood ( talk) 10:02, 5 September 2023 (UTC)
Since the style sheets of academic journals in mathematics, physics and engineering all agree since about 1920, I'm not sure why this is still so controversial.
Groupings (parenthesis, brackets, fraction bars)Unary SubtractionExponents Juxtaposition (also called implied multiplication) Multiplication and Division Addition and Subtraction - when calculations are of equal precedence they are resolved from left to right - and the clarification that multiple exponents are read from the top down — Preceding unsigned comment added by 2601:180:8300:8C50:DC15:E3C6:CE13:601F ( talk) 21:50, 13 September 2023 (UTC)
x / 2 * y
. -
Jochen Burghardt (
talk)
17:03, 14 January 2024 (UTC)
The sentence "Calculators generally perform operations with the same precedence from left to right,[1] but some programming languages and calculators adopt different conventions. " does not fit where it is placed. The order of operation should apply on mathematical rules in general and not what calculators do in general. This is very confusing because by reading this, I only care on the rules and not what calculators do. Also, in this sentence you mix calculators (what the do most), rules within programming languages which does only explain, an implementation of the rules above. What I can not read, if the rules from left to right by the order of operation is a general rule. So this article for me explains nothing.
It would be much better to have a own section for *calculator* and what the do most, then an extra section for IT and maybe which language rules per default implements different. — Preceding unsigned comment added by Goldnas ( talk • contribs) 11:24, 27 January 2024 (UTC)
60/5*3
instead typically means 12*3 == 36
.Logical OR and logical AND are non-associative and therefore should have equal precedence. Darcourse ( talk) 13:32, 31 January 2024 (UTC)
"In academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[28]"
I looked at the source, and yes, it says that multiplication is of higher precedence than division. However, it does NOT say that this is only true in cases where there is implied multiplication. The phrase "for example" implies that this source should support the previous sentence, which is does not.
The other (unlinked) sources in the paragraph again support multiplication having higher precedence than division, though whether implied multiplication is relevant is unspecified. That leaves the claim with no supporting source. 50.86.240.11 ( talk) 20:56, 7 February 2024 (UTC)
An editor recently removed this from the lead, stating that it was unnecessary.
My take is that a majority of the traffic to this page is a result of an argument over some ambiguous internet meme. I don't have anything to back this up, it's just a hunch.
Anyway, it seems worth discussing here on the talk page - should this one-sentence treatment be in the lead? I think it should. Other opinions? Mr. Swordfish ( talk) 20:50, 11 February 2024 (UTC)
Hi, Jacobolus. Your comment on your recent edit seems to be a reference to my most recent edit, but none of the things you deleted were caused by my most recent edit, which only changed a single word. I don't think I wrote anything you deleted, though I wouldn't swear to it. I have no objection to taking out all the references to the internet memes, though they may be of interest as a minor point later in the article. Rick Norwood ( talk) 22:45, 11 February 2024 (UTC)
I've been thinking about this quite a bit. Your rewrite has improved the article greatly, and as it stands, I have no strong objection. The bigger problem is that every math book used in K-12 education in the United States lies to its students. For example, they all say that parentheses are an "operation", just like addition and multiplication. And they all say that you must do parentheses first, which is impossible in a problem such as 2+3+(x+y). And they all say you must work from left to right, which is ridiculous in a problem like 283+389-283.
However, getting back to the question at hand. As you not, the problem only occurs with the use of the solidus. I've just glanced through several math books, and they almost always use a horizontal fraction like. I haven't found one that uses x/2 instead of 1⁄2x or x⁄2. Rick Norwood ( talk) 13:01, 14 February 2024 (UTC)
<math>\tfrac12 x</math>
which renders as or using {{math|{{sfrac|1|2}}''x''}}
which renders as 1/2x.)@ Mr swordfish I've made a bunch of other changes relevant to the ambiguity of multiplication/division, internet memes about it, and related topics. Does the current version address your concern, or do you still think the memes are under-discussed? @ D.Lazard, @ Jochen Burghardt do these recent changes seem okay to you, or are there parts that seem problematic? – jacobolus (t) 02:11, 17 February 2024 (UTC)
"Keep in mind that, in determining proper weight, we consider a viewpoint's prevalence in reliable sources, not its prevalence among Wikipedia editors or the general public."I think mentioning this topic at all is entirely sufficient, and promoting it to the lead doesn't seem justified to me. Maybe we should take the question to a more visible venue like WT:WPM for more feedback, if you think this seems like a controversial position. – jacobolus (t) 05:40, 20 February 2024 (UTC)
Should we be including ISO standards in the "Mixed division and multiplication"? The standards include authoritative answers to some of the questions and ambiguities, for instance 80000-2-(9.6) states that '÷' "should not be used" for division (see division sign) and 80000-1 (7.1.3) states that the solidus "shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity". Unfortunately the standards aren't freely available and I have only come across snippets that others have posted elsewhere. StuartH ( talk) 05:48, 10 April 2024 (UTC)
Cite error: There are <ref group=lower-alpha>
tags or {{efn}}
templates on this page, but the references will not show without a {{reflist|group=lower-alpha}}
template or {{notelist}}
template (see the
help page).
This is the
talk page for discussing improvements to the
Order of operations article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Archives:
1,
2,
3,
4Auto-archiving period: 365 days
![]() |
![]() | This ![]() It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||
|
There is a current version of this article that insists that a parenthesis is a mathematical operation and that PEDMAS is a law of mathematics. A parenthesis is a symbol of grouping and PEDMAS is a mnemonic. No reference is given suggesting otherwise. The person who wants this in the article has restored this claim after my revert with the comment "Take it to the talk page." I would appreciate the opinion of others. Rick Norwood ( talk) 19:21, 10 April 2023 (UTC)
1. Parentheses: any operation or series of operations delimited by parentheses or other symbols of grouping (the order of operations applies also to such grouped operations). This resolves another issue of the current version, namely that it is not said that the order of operations applies also inside parentheses. D.Lazard ( talk) 18:32, 12 April 2023 (UTC)
this once was taught in grade 1 ... back in the 60's– this was never taught in the first grade. More like 5th–7th grade. It definitely does not date to Thales or Euclid; modern mathematical notation largely arose in the 17th–19th century, and was initially not very settled. The teaching of formal 'order of operations' rules comes from the 19th century.
parenthesis are ( ) ... { } are NOT parenthesis– in this context the word "parentheses" covers all kinds of grouping punctuation. Often these are ordered from inside out as: round "parentheses" (), square brackets [], curly braces {}, and later sometimes angle brackets etc. However, in technical literature it is also common to just use nested parentheses, reserving other kinds of brackets for other purposes such as real intervals, set-builder notation, bra-ket notation, matrices, the Iverson bracket, and so on. – jacobolus (t) 01:48, 17 February 2024 (UTC)
I still think parentheses are a separate topic, which are not clearly explained by an instruction to "do them" first. You don't "do" parentheses. But there is another comment above that I'm curious about: "the term more commonly used in the rest of the English-speaking world". What term is that?
In the US, we talk about (parentheses), [brackets], and {braces} all of which are sometimes used as symbols of grouping and all of which have other uses. Parentheses are used both for points (a,b) and for open intervals (a,b) and there is no way to tell which use is intended except from context. Brackets are use for closed intervals [a,b]. Braces are use for sets {a,b} and an open brace is used for a system of simultaneous equations. (Parenthetic aside, off topic: My students are no longer taught much vocabulary in the US K-12 system, so I now have to say, instead of "brackets", "square brackets" and instead of "braces", "curly braces", for my students to know what I'm talking about.
Wikipedia should have an article titled "Symbols of grouping". I'll think about creating one. Rick Norwood ( talk) 10:41, 14 April 2023 (UTC)
I recently added a section "In popular culture" discussing internet memes with ambiguous mathematical expressions. It was reverted because "it was already covered" elsewhere. But the current coverage is buried in the middle of a subsection, doesn't provide much coverage, and cites a source that is self-published.
I don't have any stats to back this up, but my sense is that a large amount of traffic to this page is driven by these internet memes. Since our job is to serve our audience we should provide a more prominent treatment of ambiguous expressions.
I hope that the other editors will consider the since reverted section and think about how to incorporate it into the article. Mr. Swordfish ( talk) 15:56, 6 July 2023 (UTC)
Apologies in advance for being a nudge here, but I'm now wondering whether those ambiguous mathematical expressions so often posted on social media are actually memes. I used that term here on the talk page as a kind of shorthand, but did not use it in my proposed edit ( https://en.wikipedia.org/?title=Order_of_operations&oldid=1163541119#In_popular_culture).
So, are they memes? If so, then clearly they are internet memes and we can call them that. But after reading the definition of meme, I'm not convinced they are, and putting my wikipedia editor hat on, we'd need some source saying that these things are in fact memes regardless of whatever conclusion I might draw from the definitions.
So, anybody got a cite that calls these things "memes"? If not, we should change the language. Mr. Swordfish ( talk) 23:03, 9 July 2023 (UTC)
Why do we use this phrase in the Definition section?
I've looked at every single source cited in the article, and except for the non-US sources that use "Brackets" and the Wolfram cite that uses "Parenthesization" every single cite simply uses the word "Parentheses". And the Wolfram cite links their word to their article on "Parentheses.
So, what's up with us making up our own nomenclature? If there's reliable source using the phrase "Parenthetic subexpressions" we need to cite it. Otherwise, it seems fairly clear to just repeat the language that all the cited sources use. Other opinions? Mr. Swordfish ( talk) 00:04, 18 August 2023 (UTC)
At one point, I spent a substantial amount of time rewriting this article to make it mathematically accurate. Other editors immediately reverted my rewrite and reinserted incorrect information, apparently on the grounds that it was what they were taught in grade school.
I would really like not to have to continue teaching my college classes that the things they were taught in grade school are wrong, and I think good Wikipedia articles would be a step in the right direction, since most of my students use Wikipedia. But the fans of parentheses as operations rather than symbols of grouping will, as can be seen above, argue illogically and interminably.
Will anyone who actually knows something about logic and mathematics help? Or should I give up and move on to another article? Rick Norwood ( talk) 10:54, 21 August 2023 (UTC)
That would probably be an improvement, but the correct statement is this: if there is an operator both to the left and to the right of a given expression, the operator higher on the list should be applied first. If both operators are on the same level, the associative law applies, and applying either first gives the same results. The main point that it is perfectly all right to add two numbers somewhere in an expression before you perform a multiplication somewhere else entirely.
I'm going to make a change, and we'll see what happens next. Rick Norwood ( talk) 10:30, 22 August 2023 (UTC)
Ah, well. It takes a long time to do a carefully rewrite, and only seconds to revert it. Apparently, even though we all agree that parentheses are not an operation, there are enough people who want this article to say that that it keeps going back in. This time I am going to do just one thing, remove the claim that parentheses are an operation. We'll see what happens next. Rick Norwood ( talk) 19:07, 22 August 2023 (UTC)
My previous edit stood for more than an hour, so I'm going to start moving the material in this article that says nothing about the order of operations to the article titled symbols of grouping. Rick Norwood ( talk) 21:16, 22 August 2023 (UTC)
I've added references. If reverted again, I'll add another reference and restore what makes sense.
Mr. Swordfish argues that, since this is an elementary article we do not need to limit "operation" to the mathematical meaning. We can use the dictionary meaning. But the title of the article uses "operations" in the mathematical meaning, not the dictionary meaning, and so the article should do the same.
Mr. Swordfish and several others share a consensus that there is a difference between a mathematical operation and a symbol of grouping. Why, then, does he keep adding Parentheses to the list of mathematical operations? What does he think that adds to the article? Rick Norwood ( talk) 21:55, 22 August 2023 (UTC)
On the contrary. No reliable mathematical source says parentheses are operations. You are the only person who says this.
It is true that essentially all US grade school textbooks list parentheses in their order of operations. They also have many other mistakes, such as forcing students to add from left to right. The people in power, who decide the grade school curriculum, want things the way they have always been. But Wikipedia uses professional terminology, not grade school terminology. Why do you want Wikipedia to repeat grade school mistakes? Rick Norwood ( talk) 23:05, 22 August 2023 (UTC)
I've added another reference. The Common Core does not include PEDMAS. Teachers teach PEDMAS because they teach what they were taught and books include PEDMAS because teachers like it. But it is not in the Common Core and the fact that it is wrong has been pointed out many times.
I'm surprised to find D. Lazard on the other side of this question, since he is an editor I respect. I can only suggest he Google "is pedmas correct" or "is pedmas still in common core".
As for the article not saying Parentheses are operations, read the section carefully. Here is what it says:
"The order of operations, that is, the order in which the operations in a formula must be performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as:[1][5][6]
Parentheses Exponentiation Multiplication and Division Addition and Subtraction"
Clearly, the implication is that the summarized list is a list of operations.
But the main point is that the Common Core has abandoned PEDMAS, that many sources say clearly that PEDMAS is wrong, and there is no good reason to perpetuate this error. Rick Norwood ( talk) 12:30, 23 August 2023 (UTC)
This means that to evaluate an expression, one first evaluates any sub-expression inside parentheses, working inside to outside if there is more than one set.Also, an initialism, such as PEDMAS cannot be wrong by itself; the problem with it is that it can be misleading if interpreted as a list of operations (what it is not). In any case, as PEDMAS is not mentioned in the current version before section § Mnemonics, you cannnot use your opinion on PEDMAS to force modifications of sections that do not mention PEDMAS at all. D.Lazard ( talk) 13:01, 23 August 2023 (UTC)
Clearly, you have made up your mind. I wish you would at least took at the references, and the other changes you reverted, which moved discussions of symbols of grouping. As things stand, unless someone else supports the view I support, which is the view of the Common Core document, then this article will continue to mislead readers.
Yes, a consensus is important. But in Wikipedia, authoritative references are even more important. And I am pretty sure that no mathematical publication, as distinct from a grade school publication, has the list with parentheses at the top. Rick Norwood ( talk) 13:20, 23 August 2023 (UTC)
The order of evaluation, that is, ..." (change suggestion underlined). I believe to remember that recently I made such an edit, but apparently it got reverted somehow. - d Jochen Burghardt ( talk) 18:20, 23 August 2023 (UTC)
We have solid sourcing that PEMDAS is used in the US and France, and also that BEDMAS is used in Canada and the UK.
We don't have sourcing for the geographical distribution of BODMAS or BIDMAS, so I propose simply writing around the gap instead of making specific claims that are not supported by cites.
Also, the "O" in BODMAS is sometimes said to stand for "Order" (an archaic word for exponentiation), "Of" [a], in addition to the Operations that we state in the text. Seems like we should include those alternatives.
Per the above, I suggest the following text for the third bullet point:
New references are bare urls for now - we can format them in a better manner if this change is accepted. Mr. Swordfish ( talk) 14:31, 23 August 2023 (UTC)
I'll only point out (again) that the Common Core standards do not use PEMDAS. I suppose it needs to be here, since most US grade schools ignore the Common Core standards, even when their state requires them. I agree with Mr. Swordfish about shortening this section. Rick Norwood ( talk) 10:24, 24 August 2023 (UTC)
References
Syllabus_2019
was invoked but never defined (see the
help page).Vedantu_2019
was invoked but never defined (see the
help page).The article uses the term "precedence" without defining it. There are almost 20 incoming redirects that have "precedence" in their title, and many others that use the pipe [[Order of operations|precedence]]. In particular, it is almost impossible for a beginner to know which of addition and multiplication has the higest precedence.
So, a definition of precedence must be given in the lead, and this must be expanded in a specific section. Someone is willing to do that? D.Lazard ( talk) 16:42, 23 August 2023 (UTC)
Again, I agree with Mr. Swordfish. There is a Simple English Wikipedia for people who do not know the meaning of common words such as "precedence". Rick Norwood ( talk) 10:28, 24 August 2023 (UTC)
This is getting really strange. Mr. Swordfish says that in this article it is ok to use the dictionary meaning of operation, which has a special mathematical meaning. D. Lazard says it is not ok to use the common word precedence, which means "which comes first", and is not used here to mean anything else but "which comes first". Rick Norwood ( talk) 10:06, 25 August 2023 (UTC)
References
The opening sentence of the Programming languages section states:
and while this is correct, it could be misleading. My experience is that nearly every programming language uses the "standard" operator precedence (with the usual caveats above) so stating it as "Some" implies that it is not the norm, or even a majority.
Looking at this list of most popular programming languages the only exceptions that jump out as exceptions are Lisp and Haskell, which are pretty far down on the list, and html which doesn't really do math at all. Perhaps there are others since I'm not familiar with all of them, but all the more common ones use the standard operator precedence (to the extent that there is one - i.e. grouping symbols, exponents, multiplication/division, and addition/subtraction in that order; beyond that all bets are off)
I don't think it would be original research to look at that list and say "Most commonly used programming languages..." instead of "Some programming languages..." but some may argue that point. Other suggestions for how to word this to avoid possible mis-representation? Or a good cite for this change? Mr. Swordfish ( talk) 13:50, 30 August 2023 (UTC)
The second sentence of this article is:
This is certainly correct, but might be too much this early in the article. My sense is that most of our readers are not familiar with the concepts of functional or polish notation, and those systems are not what this article is about. Granted, there are links for the reader to click, but my reading (assuming the perspective of a non-mathematician) is that this sentence is a distraction from the main thrust of the article.
I'd suggest simply moving this sentence to later in the article, perhaps just a paragraph or two. Alternatively, provide a parenthetical example so the reader doesn't have to click on the link to find out that infix notation is just the familiar way of writing mathematical expressions that they have come to know and love:
Other opinions? Mr. Swordfish ( talk) 15:28, 2 September 2023 (UTC)
when infix notation is used" to "
when the usual notation (called infix notation) is used". Adding an example for infix isn't useful, except when it is contrasted with (e.g.) Polish notation; so we could possible add a sentence like "
For example, the infix expressions 3 × 4 + 5 and 3 × (4 + 5) are written as + × 3 4 5 and × 3 + 4 5 in Polish notation, respectively.". I'm afraid, however, that such a sentence won't be understood without additional (and then distracting) explanations. Maybe, reverse Polish notation is easier to explain; in fact is has been employed by HP calculators, so it may be known better. - Jochen Burghardt ( talk) 15:54, 2 September 2023 (UTC)
I am not surprised that my removing the false information "operations with the same precedence are generally performed left to right" was reverted. So many people have been taught that false "rule" in grade school that many people insist that what they learned in grade school is true. But all mathematicians know that addition is commutative and associative and multiplication is commutative and associative, and mathematicians generally perform operations in whatever order is most convenient.
It is a bit ironic that I think 12/6*2 = 4, which is what you get when you perform operations left to right. But most physicists insist that 12/6*2 = 1. Of course, my reasoning has nothing to do with left to right. It makes sense to me that subtraction is addition of the opposite and division is multiplication by the reciprocal. It is strange that after all these centuries, there is nobody who can settle the question. Rick Norwood ( talk) 10:02, 5 September 2023 (UTC)
Since the style sheets of academic journals in mathematics, physics and engineering all agree since about 1920, I'm not sure why this is still so controversial.
Groupings (parenthesis, brackets, fraction bars)Unary SubtractionExponents Juxtaposition (also called implied multiplication) Multiplication and Division Addition and Subtraction - when calculations are of equal precedence they are resolved from left to right - and the clarification that multiple exponents are read from the top down — Preceding unsigned comment added by 2601:180:8300:8C50:DC15:E3C6:CE13:601F ( talk) 21:50, 13 September 2023 (UTC)
x / 2 * y
. -
Jochen Burghardt (
talk)
17:03, 14 January 2024 (UTC)
The sentence "Calculators generally perform operations with the same precedence from left to right,[1] but some programming languages and calculators adopt different conventions. " does not fit where it is placed. The order of operation should apply on mathematical rules in general and not what calculators do in general. This is very confusing because by reading this, I only care on the rules and not what calculators do. Also, in this sentence you mix calculators (what the do most), rules within programming languages which does only explain, an implementation of the rules above. What I can not read, if the rules from left to right by the order of operation is a general rule. So this article for me explains nothing.
It would be much better to have a own section for *calculator* and what the do most, then an extra section for IT and maybe which language rules per default implements different. — Preceding unsigned comment added by Goldnas ( talk • contribs) 11:24, 27 January 2024 (UTC)
60/5*3
instead typically means 12*3 == 36
.Logical OR and logical AND are non-associative and therefore should have equal precedence. Darcourse ( talk) 13:32, 31 January 2024 (UTC)
"In academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[28]"
I looked at the source, and yes, it says that multiplication is of higher precedence than division. However, it does NOT say that this is only true in cases where there is implied multiplication. The phrase "for example" implies that this source should support the previous sentence, which is does not.
The other (unlinked) sources in the paragraph again support multiplication having higher precedence than division, though whether implied multiplication is relevant is unspecified. That leaves the claim with no supporting source. 50.86.240.11 ( talk) 20:56, 7 February 2024 (UTC)
An editor recently removed this from the lead, stating that it was unnecessary.
My take is that a majority of the traffic to this page is a result of an argument over some ambiguous internet meme. I don't have anything to back this up, it's just a hunch.
Anyway, it seems worth discussing here on the talk page - should this one-sentence treatment be in the lead? I think it should. Other opinions? Mr. Swordfish ( talk) 20:50, 11 February 2024 (UTC)
Hi, Jacobolus. Your comment on your recent edit seems to be a reference to my most recent edit, but none of the things you deleted were caused by my most recent edit, which only changed a single word. I don't think I wrote anything you deleted, though I wouldn't swear to it. I have no objection to taking out all the references to the internet memes, though they may be of interest as a minor point later in the article. Rick Norwood ( talk) 22:45, 11 February 2024 (UTC)
I've been thinking about this quite a bit. Your rewrite has improved the article greatly, and as it stands, I have no strong objection. The bigger problem is that every math book used in K-12 education in the United States lies to its students. For example, they all say that parentheses are an "operation", just like addition and multiplication. And they all say that you must do parentheses first, which is impossible in a problem such as 2+3+(x+y). And they all say you must work from left to right, which is ridiculous in a problem like 283+389-283.
However, getting back to the question at hand. As you not, the problem only occurs with the use of the solidus. I've just glanced through several math books, and they almost always use a horizontal fraction like. I haven't found one that uses x/2 instead of 1⁄2x or x⁄2. Rick Norwood ( talk) 13:01, 14 February 2024 (UTC)
<math>\tfrac12 x</math>
which renders as or using {{math|{{sfrac|1|2}}''x''}}
which renders as 1/2x.)@ Mr swordfish I've made a bunch of other changes relevant to the ambiguity of multiplication/division, internet memes about it, and related topics. Does the current version address your concern, or do you still think the memes are under-discussed? @ D.Lazard, @ Jochen Burghardt do these recent changes seem okay to you, or are there parts that seem problematic? – jacobolus (t) 02:11, 17 February 2024 (UTC)
"Keep in mind that, in determining proper weight, we consider a viewpoint's prevalence in reliable sources, not its prevalence among Wikipedia editors or the general public."I think mentioning this topic at all is entirely sufficient, and promoting it to the lead doesn't seem justified to me. Maybe we should take the question to a more visible venue like WT:WPM for more feedback, if you think this seems like a controversial position. – jacobolus (t) 05:40, 20 February 2024 (UTC)
Should we be including ISO standards in the "Mixed division and multiplication"? The standards include authoritative answers to some of the questions and ambiguities, for instance 80000-2-(9.6) states that '÷' "should not be used" for division (see division sign) and 80000-1 (7.1.3) states that the solidus "shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity". Unfortunately the standards aren't freely available and I have only come across snippets that others have posted elsewhere. StuartH ( talk) 05:48, 10 April 2024 (UTC)
Cite error: There are <ref group=lower-alpha>
tags or {{efn}}
templates on this page, but the references will not show without a {{reflist|group=lower-alpha}}
template or {{notelist}}
template (see the
help page).