Re: Cardinality of relation with empty set of attributes is 1

Aloha Kakuikanu wrote:
> Proof:
> MVFD with empty antecedent, for example
>
> {} -> {X} | {Y,Z}
>
> claims that cardinality of the XYZ relation is the product of
> cardinalities of its projection onto the sets X and YZ of attributes.
>
> Take {X} to be an empty set, then:
> {} -> {} | {X,Y,Z}
> holds trivially. Since projection to the entire set of attributes
> {X,Y,Z} doesn't really change the relation, it follows that the other
> relation in the MVFD decompostition should have cardianlity 1.

Why would that follow? The size of the projection of the empty relation on {} is 0, the size of the empty relation on {X,Y,Z} is also 0. And the product of those sizes is indeed the size of the empty relation.

• Jan Hidders