# How is a statistic represented as a mapping with varying number of arguments?

Suppose that are $n$ sample points taking values in $A$.

A statistic for sample size $n$ is a mapping from $A^n$ to another set $B$.

But $n$ can vary in $\mathbb N$. There are also similarities among the mappings with different $n$. How would you represent a mapping with varying number of arguments then? I am open to solutions or suggestions from both set theory and statistics.

Thanks and regards!

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You could simply take $A^{\lt\omega}=\bigcup_{n\in\mathbb{N}}A^n$ to be your domain if you want a single function to work for all possible sizes of input. –  Miha Habič Feb 26 '13 at 5:10