3

If $a$ is a real constant, do you regard $3a$ and $a3$ as equal or different?

String
  • 18,395
  • 4
    Equal but it is conventional to write $3a$. If you want to write $a3$ I suggest you write $a \cdot 3$ otherwise one might think $a3$ is the whole name of a single variable. – Amateur May 05 '14 at 17:39
  • @Amateur: thanks! Do you believe that any skilled mathematician would write $a3$ to mean $a\cdot 3$? – String May 05 '14 at 19:32
  • No problem! I think that no skilled mathematician would do that. – Amateur May 05 '14 at 19:41
  • @Amateur: How would you evaluate $a(b+3)$? – String May 05 '14 at 19:50
  • @String Could it be that you are making fun of people? Your many repetitive (and almost nonsensical) comments appear suspicious, to me. – mathse May 05 '14 at 20:00
  • @mathse: No! I just attended a seminar on didactics in mathematics where the professor gave us an MC sheet. One question was: Is $3a=a3$? And this was by no means meant as a trick question. He then explained about this specific question that 1/3 of the students in high school (or something similar to high school as I am in Denmark having a different educational system) answered mistakenly that they were different. He explained it by the use of CAS where he suggested that a_3 and a3 were confused. But I never saw $a3$ from a skilled mathematician prior to that. – String May 05 '14 at 20:13
  • But why are you asking the same things over and over again? And you confront individual commentators with contents from other answers ... Maybe it's possible, but simply don't write $a3$ - it is unusual, I haven't seen it and it looks like a typo for $a_3$ or $a^3$ ... Some things are just conventional like writing from left to right (at least in Western countries). – mathse May 05 '14 at 20:19
  • @mathse: And if you look carefully, I am trying to make answerers qualify their answers, but I have tried to keep an open mind in the wording of my additional comments. I might be the one who is wrong after all. I do not know if I managed to balance that succesfully. You call the comments non-sensical. How come? – String May 05 '14 at 20:20
  • @mathse: Ah, I see! My eagerness possibly came across as me being confrontatory :( That was entirely uncalled for on my behalf! I apologize to anyone who got that impression! – String May 05 '14 at 20:22
  • And the reason for asking repeatedly was rather that I expected possibly different answers; I would like to know if they differ since that would question the prominence of the suggested conventions ... – String May 05 '14 at 20:25
  • And does it need to be a typo? Why can $a3$ not be a valid name for a variable on the same level as $a_3$. In my opinion it is! – String May 05 '14 at 20:29
  • @String You are right: it is. In Matlab you can write $a3=100$. I do however think that you are either looking for attention or are indeed trying to make fun of people. – mathse May 05 '14 at 20:35
  • @mathse I don't understand your above comments. I see nothing belittling or confrontational in the OPs comments - only sincere inquiries. – Bill Dubuque May 05 '14 at 20:40
  • @BillDubuque Except that he is asking every person who comments the same things (over and over again)? – mathse May 05 '14 at 20:41
  • @mathse: That truly annoys me! Sorry, but it does. Check my questions and answers to see that I care about both mathematics and notation rather than to provoke and attract attention, and, hopefully come back and apologize for your unfair skepticism! Sorry if the tone in this comment is hard, but what can I do? – String May 05 '14 at 20:41
  • @mathse I don't agree. Rather, I see the OP sincerely (and eagerly) inquiring about imprecise parts of answers. Please try to give users the benefit of the doubt before making accusations like that. Also please keep in mind that not all users are native English speakers, so they may not phrase things in optimal ways, leading to possible ambiguities. – Bill Dubuque May 05 '14 at 20:48
  • @BillDubuque: Spot on concerning my English skills! I am Danish and trying as hard as possible. Often times I feel that I lack the correct nuanced word for a specific situation. At least I feel that I am still improving regarding that! – String May 05 '14 at 20:56
  • But @BillDubuque I'm sure if you will continue to respond to his inquiries, you will stay busy all night long because these fundamental issues of epistemology (could $a3$ be a variable? I am asking this myself now? Could it or not?) will not be resolved so quickly. – mathse May 05 '14 at 20:58
  • 1
    @String Such matters may be important epistemologically. Not every mathematician has a taste for such. But that does not mean such questions are insincere. – Bill Dubuque May 05 '14 at 21:00
  • @String Your English is great (I was making a general point). Indeed, nonnative speakers may have a harder time choosing between various nuances of language that, e.g., may help to distinguish sincerity vs. frivolity. Even native speakers have problems with such online, lacking cues like facial expressions, tone of voice, etc. – Bill Dubuque May 05 '14 at 21:05

4 Answers4

6

Both are technically correct, but convention is to write $3a$, not $a3$. If you write $a3$, it could be mistaken for $a_3$ or $a^3$. Not following convention in mathematical writing is like using poor grammar in English.

Logan Tatham
  • 2,522
  • Thank you! Is this convention so prominent that $a3$ would be considered wrong? How is such a convention even known to be agreed upon? Is it a non-articulated rule or did someone state it specifically? Could $a3$ be a valid name for a mathematical object or does it have to be subscript $a_3$? – String May 05 '14 at 19:30
2

If $3$ and $a$ were both elements in a non-Abelian group, it would be possible that $3a \ne a3$. The convention helps to emphasize that you're working in a set with commutative multiplication.

grantfgates
  • 656
  • Which convention are you alluding to? – String May 05 '14 at 19:36
  • The convention that $ab=ba$ when we deal with a set where multiplication is commutative. – Sujaan Kunalan May 05 '14 at 20:03
  • Ah, ok! But does that imply the same notational rules for mixes of numbers and letters? After all we do not write $34$ and $43$ for the commuting product of $3$ and $4$, so at least writing purely numbers differ in this sense. – String May 05 '14 at 20:52
2

With usual conventions $\ 3a = a + a + a = a3.\ $ However, the latter might prove confusing because of the widespread convention to write "coefficients" before "variables" in expressions having polynomial form. This is part of the algorithm that leads to the standard normal form for polynomials $\,c_0 + c_1 x + \cdots+ c_n x^n\,$ with coefficients on the left. Because polynomials are ubiquitous, so too is this convention (or normal-form).

Bill Dubuque
  • 272,048
  • Thanks! Have you ever seen a skilled mathematician choose to write $a3$ rather than $3a$? – String May 05 '14 at 20:16
  • @String Yes, I do it on occasion when it helps to highlight structural similarity, e.g. when specializing variables in a general formulas while maintaining the same structure. I've also seen others do likewise. But most probably would not do so in a formal publication (though they might write $,a\cdot 3).$ – Bill Dubuque May 05 '14 at 20:19
  • Thanks for your reply! Would those mathematicians add some space then like in $a\ 3$ or not bother if they write them close together as $a3$? – String May 05 '14 at 20:31
  • @String I don't recall. Why is that of interest? If you provide further context for your question that may elicit more helpful answers. – Bill Dubuque May 05 '14 at 20:35
  • Sorry, only because I myself read $a3$ as most probably being a variable name. But just because I have not seen mathematicians write $a3$ for multiplication, it does not mean that my didactics professor is wrong. There are certainly so many things I haven't seen, including in the field of mathematics! – String May 05 '14 at 20:45
  • And I enjoy programming too where $3a$ would produce "syntax error" and $a3$ would certainly be a variable name ... – String May 05 '14 at 20:49
  • I accepted your answer as both the answer and your various comments gave me a nuanced account of conventional use vs. special uses for special occasions. That said, I do not believe that any closed answer to this question is possible. Thank you all of you for your time and effort! Including @mathse, disregarding out controversies ... – String May 05 '14 at 21:27
  • 1
    @String You might also find of interest section 7.4 (Spaces mean Multiplication) in R. J. Fateman's A Review of Mathematica. Better answers may well appear. If so, don't hesitate to accept them instead (generally users accept too quickly). – Bill Dubuque May 05 '14 at 21:27
  • Very nice! I shall read that! – String May 05 '14 at 21:29
  • @ You two. It's almost a pity that you finished, there was something burlesque to your discussion. Btw. I like how this programming handbook section 7.4 starts with the words: "This is perhaps a minor point, but annoying in its own way." :) – mathse May 05 '14 at 21:52
  • @Mathse I don't see anything "burlesque" above (except perhaps your reference to RJF's review as a "programming handbook"). – Bill Dubuque May 05 '14 at 22:00
  • Another point is if you read them out loud. Then "three a" and "a three" may be concieved of as operation and variable name respectively from the sound of it ... – String May 05 '14 at 22:00
  • 1
    @mathse: If you question the relevance of my question in the first place, I'm ok with that! It was the attack on me as a person I did not understand! – String May 05 '14 at 22:04
  • @BillDubuque Oh, yes, you are right. The great RJF's review of Mathematica. This is of course not a programming handbook but merely a review of Mathematica. It is unfortunate you don't see anything burlesque above, I do. – mathse May 05 '14 at 22:10
  • @mathse: After consulting Cambridge Advanced Learners dictionary, having learnt a new word - what in particular do you think make which serious matter seem stupid? And is that a relevant comment regarding the original question or just bullying? – String May 05 '14 at 22:32
  • 1
    @String To quote my old linear algebra professor (no, it was not RJF, but he was nonetheless referring to Mathematica or Matlab, I think): "If you have no friends, you can be busy with this all day." In this sense, I wish you a good night or evening. – mathse May 05 '14 at 22:42
1

It's just how everyone has agreed to write it(3a). If you want to write it like a3 then I would make it (a)(3) so people know we are multiplying things.

King Squirrel
  • 2,607