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This is blatantly a terminology question, but it's bugging me.

If a comma is used in French to separate the one's and tenth's place, e.g. $5/4=1,25$, how do you write the ordered pair $(5/4,6)$?

Surely $(1,25,6)$ is ambiguous since it could be interpreted as $(5/4,6)$ or $(1,256/10)$? What do they do in school there?

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    $\begingroup$ And how do non-French people know if $(2,3)$ is an ordered pair or an open interval? (By the way, your $25/6$ isn't right. :)) $\endgroup$ Commented 2 days ago
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    $\begingroup$ @TedShifrin an ordered pair, an open interval, or the greatest common divisor. For those context indeed suffices, but not so obviously in the example I presented. Maybe they don't use a comma for ordered pairs? I want a real answer. A student came to my school from a french educational background with weak English/math skills and seemed to be getting confused doing some problems. I want a genuine and serious answer about what they actually do in France. $\endgroup$ Commented 2 days ago
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    $\begingroup$ France is not the only place that has (historically) used a comma as a separator for decimal fractions. What they do in France is of course directly relevant to the purpose of the question (which I suggest editing into the question itself), but I imagine the same notational problem has occurred in other countries (at least in the past) as well. $\endgroup$ Commented 2 days ago
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    $\begingroup$ I don't know about France, but Hungary uses the comma as a decimal separator, and semicolons to separate elements of an enumeration, e.g. the set denoted as $\{1,\! 5; 2; 2,\! 5\}$ hs three elements: $\frac{3}{2}$, $2$ and $\frac{5}{2}$. $\endgroup$ Commented 2 days ago
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    $\begingroup$ In purely math settings, decimals are rarely used. I don't know what they do in more practical settings. $\endgroup$ Commented yesterday

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There is no ambiguity. There are no spaces before or after a decimal comma. $$(1{,}25, 6) = (1.25, 6)$$ $$(1, 25{,}6) = (1, 25.6)$$ It is the same for handwritten text. Use correct typography. Only with a longer list of many decimal numbers with thin spaces inside numbers, should semicolons be considered for easier readability.

By the way, various English-speaking countries use a comma for separating thousands, so the "problem" would still be present. $$(10,100, 10) \text{ is a triple}$$ $$(10{,}100, 10) = (10\, 100, 10) \text{ is a pair}$$ $$(10, 10{,}010) = (10, 10\,010) \text{ is a pair}$$

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    $\begingroup$ Indeed. This is really a typographical / Latex question. The real answer is simply that Latex by default does not handle decimal commas correctly, unless instructed otherwise by either using an appropriate package or by writing {,}. Accordingly, decimal commas and separator commas look alike in Latex code written by people who do not know how to write decimal commas in Latex. That's a Latex issue though, not an issue of not being able to tell decimal commas from separator commas. $\endgroup$ Commented yesterday
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    $\begingroup$ Thanks for the insight. "various English-speaking countries use a comma for separating thousands": sure, though in practice those commas are always optional and are dropped whenever they become inconvenient. You'd only ever see $(10, 10010)$ and not $(10,\ 10{,}010)$. $\endgroup$ Commented 9 hours ago
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If there might be an ambiguity in notation with a list of decimal values, we use a semicolon, e.g. $\{2{,}3\ ; 5\}$, but this separator is often replaced by a simple comma when there is no ambiguity, e.g. with an interval $[x, 1]$.

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We (in Germany) use the comma in banking/accounting and as the official decimal separator in numbers, but the mathematicians and physicists use the dot as soon as they have left high school and are writing in English, so there is no ambiguity.

The Austrian book https://www.oebv.at/flippingbook/9783209068224/77/ uses commas. The German article https://numerik.mi.fu-berlin.de/matheon-G8/comaBuch.pdf uses commas in the text but dots in Tables 5-7. The German article https://www.fim.uni-passau.de/fileadmin/dokumente/fakultaeten/fim/lehrstuhl/sauer/geyer/NumDidaktik.pdf uses dots. The web page https://inf-schule.de/information/darstellunginformation/binaerdarstellungzahlen/exkurs_andere_zahlen/konzept_kommazahlen uses a dot in a graph and otherwise commas. The middle school article https://ddi.uni-wuppertal.de/archiv/madin/material/materialsammlung/mittelstufe/binaer/ab_03_gleitkommazahl.pdf uses commas.

One may note that the decimals after the dot/comma are in German commonly described as "die Stellen hinter dem Komma" and less often "die Stellen hinter dem Dezimalpunkt".

In computations one must follow the coding standards, and the comma is almost always used for separation in lists etc., so the dot is the decimals separator in floating point numbers. [Albeit I had a case where Java stringified with commas because the Locale was set to German..]

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    $\begingroup$ I think the question is not "What do French mathematicians write" (despite the title saying so), but "What do mathematicians write in French". This answer essentially says "German mathematicians do not write in German", which may be mostly true in 2025 (is it true at an undergraduate level in university?), but evades the question. Or do undergraduates and others use English number notation even in German language texts? $\endgroup$ Commented 19 hours ago
  • $\begingroup$ the generalization is untrue and uncalled for. The question also is about the common separator for pairs or tuples, which is a semicolon ; or a pipe | , rarely a comma (at least during my time in university), unless the "values" are just letters. As soon as one uses numbers, the comma was shunned, even in English writing. $\endgroup$ Commented 11 hours ago
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We (Finland) also use comma as a decimal separator in common contexts (outside academia, for example in price tags and such). It doesn't really cause confusion for most people.

  • My students are free to use the period as a decimal separator. They get used to the alternative at an early enough age given that most pocket calculators use the period.
  • Spacing is different. A pro-tip for TeX use: if you write $2{,}3$, it is typeset as $2{,}3$ and you can see the difference in spacing. Recycling your example: $(1{,}25,6,0)$ vs. $(1{,}25, 6{,}0)$. Not very clear (particularly when handwritten). Another possibility is to add thinspaces: $(1{,}25,\,6,\,0)$ vs. $(1{,}25,\, 6{,}0)$.
  • I do concede that the difference is a problem, when using some pieces of software like Microsoft Excel. You always need to remember that if you running a Finnish language version (don't remember exactly what the setting is called), then, in its infinite wisdom, MS uses a comma exclusively as a decimal separator, and a semicolon as a list separator. When you search for syntax help within Excel, you need to remember not to just copy/paste snippets because it will be misinterpreted.
  • I have occasionally, when needing to print a sequence of decimal numbers inside parens, also used semicolons as separators. Basically to make the meaning clear to me students. As others explained, this is rarely needed in math courses. Engineers and/or physicists may meet this problem more often than math teachers. Anyway $(1{,}25;\, 6;\, 0)$ and $(1{,}25;\, 6{,}0)$ are quite unambiguous.
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    $\begingroup$ "When you search for syntax help within Excel, you need to remember not to just copy/paste snippets because it will be misinterpreted." Because of things like this, I think it's a good idea to avoid internationalized locale settings when programming (although I didn't realize spreadsheets would also be affected.) This is true even for English speakers -- the modern "en_US" locale has different sorting from the traditional "C" locale, and it causes compiler errors to use curly "smart" unicode quotes instead of straight ASCII quotes, and other such nonsense. $\endgroup$ Commented yesterday
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    $\begingroup$ Excel is worst! Not only does it translate numbers, but it translate function names as well. How are we supposed to remember that MROUND becomes ARRONDI.AU.MULTIPLE and that BITXOR becomes BITOUEXCLUSIF?! $\endgroup$ Commented 12 hours ago
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In Brazil, we also use commas to separate the units and tenths places. I don’t remember a single instance where this ambiguity actually caused confusion.

Outside academia, I suppose people rarely need to write lots of pairs of real numbers in decimal notation.

In academia, during my Bachelor’s in Mathematics, except perhaps in physics, experimental physics, numerical calculus and statistics, we were expected to carry out all calculations with full precision. The exercises were designed so that you could solve them by hand, without using calculators or computers. As a result, we almost always used fractions in analytic geometry, linear algebra, multivariable calculus, and so on. The same practice continued throughout my Master’s and Ph.D. in Mathematics. For better or worse, this is often still true today, even for students from other majors taking Calculus, Linear Algebra, and similar courses.

I believe this is, to some extent, a French influence on our undergraduate and graduate education, but I could be wrong.

Of course, if one adopts the convention of writing at least one decimal place to the right of the units digit, the ambiguity disappears completely, even for triples and $n$-uples:

$$ (1,25,6,0), $$

Integer rarely appeared in experiments/numerical calculus anyway. It is likely we used tables of $x$ and $y$ coordinates separated by vertical lines, instead of pairs of points.

We could just put extra space to separate the numbers from the parentheses and the comma in the middle (and perhaps using slightly enlarged commas)

$$ (\ 1,25 \ \text{,} \ 6 \ ), $$

$$ (\ 1,25 \ \text{,} \ 6,0 \ ), $$

or perhaps we use dots instead. Everybody would understand with no issue.

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In true mathematics, I seldom used ordered pairs with raw numeric decimal numbers inside. If I correctly remember, fractions or rational numbers were much more common. But in the rare use cases where it could be required, I just used a different separator, generally a semicolon (;) to avoid any ambiguity.

But for your question, the correct presentation for a French mathematician would certainly be:

$$\left ( \frac 5 4, 6 \right )$$

Because even it $\frac 5 4 = 1.25$ is exact, what about $\frac 4 3$? And what could be the reason for a special processing when the denominator of a rational has only $2$ and $5$ as divisors?

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Here in Austria, we also use the comma: 5/4 = 1,25.

For tuples we use spacing: (1,25, 6,4, 5,3)

Or semicolon: (1,25; 6,4; 5,3)

In schools, we use | (or /): (1,25 | 6,4 | 5,3)

and sometimes sloppy (1,25 / 6,4 / 5,3)

but (1,25 | 6,4 | 5,3) would be the "correct" standard at school.

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