Definition:Vacuous


 * Logic:
 * A vacuous truth is a statement about a collection of objects none of which exist. By definition, such a statement is understood to be true.


 * Set Theory:
 * The vacuous set is the same thing as the empty set, that is, the set with no elements. This Empty Set is Unique.


 * Algebra:
 * A vacuous summation is a summation over an empty set of summands. Such a sum has a value of zero.
 * A vacuous product is an expression in product notation over an empty set of multiplicands. Such a product has a value of one (not zero).

Also see

 * Definition:Empty
 * Definition:Trivial