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In the Anglosphere (and in Russia, my home country) some of the symbols used in mathematics are the 26 letters of the English alphabet (52 actually, because there are two cases), and not any other alphabet based on the Latin script. I am aware that Greek and Hebrew, and even the Russian Ш (I call it Russian and not Cyrillic as it was introduced in honor of a Russian mathematician) letters are used in math as well.

My question is: Is this practice universal for all countries, even those that officially use an alphabet based on the Latin script (with letters not present in the English alphabet)? In other words, is there a country in which at least one Latin letter is used routinely in higher (this is important, I'm not asking about high school math) math that would not normally be considered an English letter?

I believe the answer is most likely "yes" (to the first formulation of the question) because the vast majority of mathematical papers and the leading mathematical literature are in English. Plus, English is the global lingua franca. However, I am not completely sure.

N.B. The second time derivative of $o$, i.e. $\ddot o$, is not the same as the German letter 'ö'. I know that this example is from physics, the example is just to get the point across. Also: to those that believe French uses the English alphabet, the Wikipedia article about the English alphabet disagrees (on the right it says "Languages: English" with no French or any other language in sight).

postmortes
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Alex
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    Even in English I have seen Latin letters in several variants, Greek letters, and a few Hebrew letters. – Brian M. Scott Dec 30 '20 at 03:31
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    Is there a specific example of a non-English alphabet based on the Latin script that you are curious about? – Lee Mosher Dec 30 '20 at 03:36
  • But the French language uses the exact same set of 26 letters as the English alphabet... – Lee Mosher Dec 30 '20 at 03:40
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    Your question is beginning to sound like a moving target, which makes it rather unclear and impossible to answer. Can you be more specific about what exactly you are asking? – Lee Mosher Dec 30 '20 at 03:43
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    @Alex: Technically a letter plus diacritic is not a different letter: it is a letter with a decoration. French alphabetizes e and é together, as German does with o and ó. In Icelandic, on the other hand, o, ó, and ö are alphabatized separately, as distinct letters. – Brian M. Scott Dec 30 '20 at 03:52
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    It is not correct to say that letters of English alphabet are used. Math uses the letters of Latin. English uses Latin. So what is your question exactly: Are other letters except of Latin letters used? Sure, many Greek letters are used also used: In US, UK, France, Russia etc. – mentallurg Dec 30 '20 at 03:53
  • What are some examples of Hebrew letters? – the_fox Dec 30 '20 at 04:09
  • @Alex: What you mean by "if you believe"? This is the reality. Latin and Greek letters are used since hundreds of years in many countries. It is a de-facto standard. If you want to be understood internationally, you have to use them. – mentallurg Dec 30 '20 at 04:18
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    It is not true in general that a letter plus a diacritic is technically not a different letter @BrianM.Scott . In Croatian (and similar Slavic languages from the Balkans) c, ć and č are all different letters, and even composites like dž, lj or nj are individual letters. They're not even in the same articulation group as their non-decorated cousins (e.g. ć and č are palatals and c is a dental). – Randy Marsh Dec 30 '20 at 04:33
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    This may be relevant: https://math.stackexchange.com/q/165368/139123 – David K Dec 30 '20 at 04:34
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    @RandyMarsh: You misunderstand. In Croatian those are indeed different letters, because they are treated as different letters; a simple test, as I indicated, is that they are alphabetized separately. In German, however, ö is ‘merely’ a decorated letter. The same diacritic can make a new letter in one language and what I’m calling for convenience a letter plus decoration in another. And yes, I do know something about this: I used to hang out on Usenet with a leading grammatologist, and have actually studied the subject a bit. – Brian M. Scott Dec 30 '20 at 04:43
  • I’m voting to close this question because IMHO it should be migrated to the SE site https://hsm.stackexchange.com/ – Hanno Dec 30 '20 at 10:09
  • @Alex I would go for Flagging for Moderator's attention & ask for migration to hsm.SE . Flagging is done by click in (the list in) the lower left corner of your post. – Hanno Dec 30 '20 at 10:23
  • Do not vandalise your question like this, please. There are answers to this question which are invalidated by you removing the question. – postmortes Dec 30 '20 at 10:29
  • @postmortes you can bring back the question (I don't really care), but don't tell me what to do. – Alex Dec 30 '20 at 10:32
  • @Alex are you not a native English speaker then? I apologise, from my reading of the question I thought you were. The ",please" at the end of the first sentence makes it a request, not an instruction,. – postmortes Dec 30 '20 at 10:33
  • @postmortes I'm not a native speaker, but I speak the language fluently and I'm not blind. To make it a proper request and not half-command, put the "please" before your request and don't put an emphasis on "not". – Alex Dec 30 '20 at 10:35
  • Alex: clearly we disagree; forgive me for seeming to be rude. – postmortes Dec 30 '20 at 10:36
  • @Alex Don't get discouraged by this site. And hang on to contribute, please ... $\ddot\smile$ I'd think that your current contribution feels more comfortable with the HSM site. – Hanno Dec 30 '20 at 10:36
  • @Alex: You are looking for "at least one Latin* letter ... that would not normally be considered an English letter". Latin letter that is not English letter? This sentence has no sense. There are 26 (52) Latin letters and each* of them is also an English letters. A, B, C, ..., Z are Latin letters and all of them are also English letter. I think you mean something other than you have written. Can you please explain what you mean? – mentallurg Dec 30 '20 at 19:03

2 Answers2

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I think the short answer is yes.

Decorated letters from $a, \ldots, z$ are very often used, like $i'$, but diacritic marks as found in French or German writing would be pretty unusual to be used as variables or parameters in math. While $\tilde{n}$ could be used, and it looks Spanish, it really isn't since you could just as easily find $\tilde{x}$ or $\tilde{m}$ in math and those don't correspond to any real language.

I suspect the habit goes back to the wide use of Latin until the 1800s for writing math. So I would say the trend is really the use of letters from Latin rather than from English (allowing that $j$, $u$, and $w$ came later), but I don't want to get sucked into whatever rabbit hole you've fallen into arguing with other people in the comments about what language the alphabet $a, \ldots, z$ belongs to.

The only Cyrillic letter used systematically in math outside of Russia is Ш, although you know that В, Р, and Г may be used by your own instructors if they talk about graph theory.

KCd
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    Not quite. There are at least 2 Russian letters that are widely used internationally, "Ш" and "Ж". – mentallurg Dec 30 '20 at 05:05
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    @mentallurg I did already mention Ш in my answer. As for Ж.... is that in physics or mathematics? I've never seen Ж used in math, even in Russia. Your answer mentions Ж in optics, which is part of physics. While there is a lot of overlap between math and physics, I've never thought of optics as part of math. And why would Ж be used for a something named after Lagrange? It's the last latter in the Russian spelling of Lagrange, but that would be a bizarre explanation. – KCd Dec 30 '20 at 05:36
  • Please look at the current version of the question: "is there a country in which at least one Latin* letter ... that would not normally be considered an English letter"*. Latin letter that is not English letter? – mentallurg Dec 30 '20 at 19:07
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    @mentallurg the intention behind the OP's question is clear to me: it is asking about the use of a letter in mathematical formulas from a language whose alphabet is based on the Latin/Roman alphabet but the letter is not used in English. I prefer not to get dragged into a long discussion about the OP's intentions. – KCd Dec 30 '20 at 19:15
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The answer is NO.

It is not quite correct to say that letters of English alphabet are used. Math uses the letters of Latin. The Latin is not changing since many hundreds of years.

English alphabet is based on Latin. English had letters that are partially different from Latin, see old English Latin alphabet. Later on English alphabet has changed and is currently the same as Latin. Thus, despite they look now the same, it is more correct to say that Latin letters are used, no English.

Besides Latin letters, also Greek letters are widely used in mathematics: In USA, UK, France, Germany, Russia, as well as many other countries.

Greek: Here is an example of internationally understandable notation of limit that uses Greek letters "sigma" and "delta".

German: For instance, for "power set" an old-German letter is used which is similar to Latin P. Here are example 1 and example 2.

Russian: The two widely used **Russian letters are "Ш" (sha-function, from Шафаревич), see example, and "Ж" (one of notations for Lagrange related expressions), see example.

Here is a good article about the history of mathematical notation.

  • @Alex: "and not any other alphabet based on the Latin" - This means you exclude any other, i.e. you exclude Greek. Now you added Greek in the next sentense. Thus your 1st sentence contradicts to the 2nd one. Edit your question, make it clear, remove contradiction. Then you will get some other answer. – mentallurg Dec 30 '20 at 04:23
  • OK, adjust your question according to your comment (comments can be deleted at any time, and only question and answers remain). Give an example what is included, what is not included. – mentallurg Dec 30 '20 at 04:30
  • @Alex: If by any you mean that you don't exclude Greek, does it mean that you don't exclude other languages? If don't exclude any languages, then it means you mean all languages. Then it is not clear, what is the purpose of mentioning Latin and English. – mentallurg Dec 30 '20 at 04:33
  • @Alex: May be it is clear to you. To me it is not clear. For instance, "and not any other alphabet based on the Latin". German is based on Latin. 26 (52) letters in German are the same as in Latin. Thus if one uses letter "a", it is impossible to say that it is not contained in German. Thus your statement "not any other" contradicts to other part. Pleas try to clearly formulate what you mean. Give examples what you include and what you don't include. – mentallurg Dec 30 '20 at 04:43
  • @Alex: The purpose of Stack Exchange is to provide questions and answers that are useful not to a single person asking the question, but to the whole community. Based on the number of questions in comments we see that I am not the only one who does not understand what you mean. If you want to make your question helpful, please make it clear. And you have not answered my recent questions. – mentallurg Dec 30 '20 at 04:47