I am reading some notes on correspondences and have a question. (The notes are here.) I have a question about something on page 1.
Basically, the notes provide some motivation for why we might want to define correspondences. It then says,
We would like to have a notion of a set-valued function. The seemingly obvious idea a function $f : X \to 2^Y$ from a set $X$ in to the set of subsets of $Y$ may not be the best choice.
I have looked at this several times but have no idea where the $2^Y$ comes from. Any help would be appreciated!
P.S. This actually is not homework but I am not sure what tag to use, I tried correspondences and looked through the first 5 pages of common tags without any luck.