Definition:Vacuous

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Vacuous may refer to:

• 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 an expression in sum notation 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.