# Mathematical notation around the world

What are the differences in mathematical notation around the world? I know that in some other countries they write 1,2 meaning 1.2, but what else can be confusing in an academic environment (when people are doing math on a board or on paper).

• some guys (from England I guess) even write $1\cdot 2$ to mean $1.2$. strange! Nov 29, 2013 at 17:55
• @000 that can be quite confusing indeed, since $\cdot$ is (at least sometimes/somewhere) used as multiplication instead of $\times$ Nov 29, 2013 at 18:09
• math.stackexchange.com/questions/298957/… Nov 29, 2013 at 18:19
• I think it is less probable to find differences in rather modern academic parts of mathematics, as there are limited widely used textbooks and scientific publication makes things more similar. Nov 29, 2013 at 18:22
• Actually the "British" centred decimal is like $1\!\cdot\!2$, with no spacing, which was easy to typeset but is laborious in the LaTeX era. Nov 29, 2013 at 21:48

As seen here, in some countries a diagonal bar is used before the function to denote evaluation (not sure if it's in general or just in the integration case). That is: $$\int_{0}^1 x\,dx=\mathop{\Big/}\nolimits_{\hspace{-2mm}0}^{\hspace{1mm}1}\frac{x^2}{2}$$ is used instead of what many users here would find to be the convention: $$\int_{0}^1 x\,dx=\frac{x^2}{2}\mathop{\Big|}\nolimits_{0}^{1}.$$

Then you also, of course, have different ways of denoting derivatives - Leibniz', Euler's, Newton's, etc...

Long division has different notations in different countries.Wikipedia has examples: Long division in Wikipedia

I've noticed that Anglo-Saxons use $\displaystyle{n\choose k}$ instead of $C_n^k$ for combinations or binomial coefficients. Also, repeated decimals are placed between (...) instead of being overlined, which helps avoid errors.

• It is not just the Anglo-Saxons. By the way, these are not combinations, they just count combinations. You don't call $n!$ a permutation either. Nov 30, 2013 at 11:25
• The left symbol is more or less standard notation, actually this is the first time I see the right symbol. Nov 30, 2013 at 13:12
• @ooo: QED. :-) In most European countries, it's pretty much the other way around. The symbol on the right is the standard, and the one on the left usually means a matrix or vector. Nov 30, 2013 at 15:13
• @MarcvanLeeuwen: But they are called combinations. :-) Really. Nov 30, 2013 at 15:15
• @Lucian I don't agree (under the assumption that Germany is a European country), though the distinction from a column vector is indeed hard. Apr 19, 2014 at 20:25

Function composition, in the context of group theory (a permutation is a bijection from a set onto itself), can be written

$$(fg)(x)=f(g(x))$$

Or

$$(fg)(x)=g(f(x))$$

The latter seems to be (or have been) used by some anglo-saxon mathematicians, and appears in books by Burnside, and Passman.

Also, matrix transpose is denoted $^tA$ in France, while it seems to be $A^T$ mostly everywhere else. This can be confusing when you write a product: $AB^TA^{-1}$ is of course not the same as $AB^tA^{-1}$.

• Interesting what you say about Burnside. Btw the matrix transpose notation is used also in Fischer's Lineare Algebra, which is unfortunately a standard book in Germany (unfortunately because he does not even prove the existence of bases, the book is really terrible). But maybe this is just a coincidence as this guy basically invents his own notation. Nov 30, 2013 at 13:23