Some formal characterization is seems very abstract for me.
For instance:
Let $X$ be a finite set of alternatives. We denote by $\chi$ (respectively, by $B$) the collection of all non-empty subsets (resp.,of all binary subsets) of $X$. A choice function is a mapping c:$X$→$\chi$ such that c(A)∈ A. That is, a choice function c assigns to every non-empty set A ⊆ X a unique element c(A)∈A. (Apesteguia & Ballester 2013)
What is the best way to understand this kind of characterization. Namely, i interpret this statement as below:
Let's say: $X$ ={a,b,c,d,e,f,g}
$\chi$={(a,b),(c,d),(e,f)}
What is exact interpretation of mapping statement at there?
Thanks