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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3some guys (from England I guess) even write $1\cdot 2$ to mean $1.2$. strange! – Alexander Grothendieck Nov 29 '13 at 17:55
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@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
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http://math.stackexchange.com/questions/298957/why-do-certain-notations-differ-around-the-world – hhsaffar Nov 29 '13 at 18:19
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1I 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
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1Actually 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
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@hhsaffar Agreed, cultural diferences are likely to disappear as time passes, and it's what can observe in France for combinations and matrix transpose, for example. – Jean-Claude Arbaut Nov 30 '13 at 11:23
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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...
hejseb
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Long division has different notations in different countries.Wikipedia has examples: Long division in Wikipedia
hhsaffar
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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.
Lucian
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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
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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
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2@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
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1@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
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@HagenvonEitzen: It is. But so are France and Russia, along with other Slavic countries and Romania. – Lucian Apr 19 '14 at 20:31
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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 $AB^tA^{-1}$.
Jean-Claude Arbaut
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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