# 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 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**.

- 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**.