# 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).

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some guys (from England I guess) even write $1\cdot 2$ to mean $1.2$. strange! –  Alexander Grothendieck Nov 29 '13 at 17:55
@000 that can be quite confusing indeed, since $\cdot$ is (at least sometimes/somewhere) used as multiplication instead of $\times$ –  Algebraic Pavel Nov 29 '13 at 18:09
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. –  hhsaffar Nov 29 '13 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. –  John Bentin Nov 29 '13 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...

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

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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.

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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. –  Marc van Leeuwen Nov 30 '13 at 11:25
The left symbol is more or less standard notation, actually this is the first time I see the right symbol. –  Alexander Grothendieck Nov 30 '13 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. –  Lucian Nov 30 '13 at 15:13
@MarcvanLeeuwen: But they are called combinations. :-) Really. –  Lucian Nov 30 '13 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. –  Hagen von Eitzen Apr 19 '14 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 $AB^tA^{-1}$.

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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. –  Alexander Grothendieck Nov 30 '13 at 13:23