 AC1 can be reformulated in terms of indexed or variable sets. An indexed collection of sets  \(\sA = \{A_{i}: i \in I\}\)  may be conceived as a variable set, to wit, as a set varying over the index set \(I\). Each \(A_{i}\) is then the “value” of the variable set \(\sA\) at stage \(i\). A choice function on \(\sA\) is a map \(f: I \rightarrow \bigcup_{i\in I} A_{i}\) such that  \(f(i) \in A_{i}\) for all \(i\in I\).  A choice function on \(\sA\) is thus a “choice” of an element of the variable set \(\sA\) at each stage; in other words, a choice function on \(\sA\) is a variable element of \(\sA\).  AC1 is then equivalent to the assertion