G'day,
The comparability rule for functions from the SS book are as follows:
Two functions f and g are comparable iff (i) their domains are comparable
and (ii) if their domains are equal, then f [x] and g[x] are comparable for
every element x in their domain.
Is there a specific reason for them to be so strict other than simplicity? As far as I understand the existence of a single x for which f[x] # g[x] would in theory make them distinct (and thereby comparable).
Similarly for sets (of known structure) the existence of a single element in one of the sets that is not in the other one would make them distinct.
Cheers,
Benjamin