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 set is unique.


 * Algebra: A vacuous summation is a summation over an empty set of summands. Such a sum has a value of zero.


 * Algebra: 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).

The word vacuous literally means empty. It derives from the Latin word vacuum, meaning empty space.