An empty sum is a sum indexed by the empty set. Its value is defined to be the additive identity 0, so
 |
where 
denotes the empty
set. This convention makes the rule for adding sums over
disjoint sets valid when
either set is empty.
The logical analog is an empty disjunction, whose value is false, the identity element for OR. By comparison, an empty conjunction is true, as in vacuous truth, and corresponds to an empty product equal to 1.
