The function from an empty set (which is a function called „empty function“), namely $f: \emptyset \to A$, results in $f = \{\emptyset\}$.
The function into an empty set from a non-empty set B, namely $g: B \to \emptyset$, is not a function and therefore the set $g = \emptyset$.
Is this correct?
Can there be a case where some function h is even undefined, like we know it with the division of zero, resulting in $h = undef.$ (apart from the trivial case that the function is not precisely defined, e.g. because someone had a bad hand writing)?
Best Answer
May be this is what you have in mind: The set of all functions from the empty set to $A$, $\{f\mid f:\emptyset \to A\} = \{\emptyset\}$, because there is only one function from $\emptyset$ to $A$, the empty function $f=\emptyset$.
On the other hand, the set of all functions from a non-empty set $B$ to the empty set, $\{g \mid g:B \to \emptyset\} = \emptyset$, since there's no such functions.