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The following is the standard notation for function composition of a single variable: $(f\circ g)(x)=f(g(x))$.

But is there common notation for the following: $f_1(f_2(x,y_1),y_2)$ when I have $N$ such functions? Here, $f_n: \mathbf{R}^3 \times \{1,2,3\} \rightarrow \mathbf{R}^3 \times \{1,2,3\}$.

ToniAz
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  • You could write the domain and range of the functions, that would help to understand your question. – Lucas May 22 '19 at 20:32
  • To cover everything, you need some standard tools, such as projection from $\Bbb R^n$ (or whatever factors your combined domain has) to its single coordinates and combining functions. One might write something like $f_1\circ(f_2\circ (\pi_1\times \pi_2)\times \pi_3)$ – Hagen von Eitzen May 22 '19 at 20:32
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    @Lucas Thank you for the comment. I have edited my question accordingly. – ToniAz May 22 '19 at 20:37

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