TITLE: What is the product of the empty set?
QUESTION [7 upvotes]: Give:
$fn(S)=\prod_{x\in S}x$
what is:
$fn(\emptyset)$
I can see reason that it would be defined as 1 or 0.

Note: I thought about restricting the domain of $S$ but that would make the problem less general. If there is no general answer then answers for restricted domains would be valid.

REPLY [4 votes]: If you want obvious relation $fn(A\cup B) = fn(A) \cdot fn(B)$ for disjoint $A,B$ to hold, then you don't have any choice, empy product must be multiplicative identity.