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!