DEV Community

Samuel Kendrick
Samuel Kendrick

Posted on

1

The Cartesian product of a set and the empty set

The cartesian product is the product of two sets. The resulting product is a set of pairs, one element belonging to AA and one element belonging to BB .

This can expressed as:

A×B={(x,y):xA,yB} {A \times B = \{ (x,y) : x \in A, y \in B \} }

So what happens if we try to take the cartesian product of a set and the empty set? A×{A \times \emptyset} ?

We end up with: A×={A \times \emptyset} = \emptyset . This is because we try to build a set like this: A×B={(x,y):xA,yB}{A \times B = \{ (x,y) : x \in A, y \in B \} } , but BB is empty.

It is impossible to create this resulting set of pairs because one of the sets is the empty set. As such, not a single element can be produced from BB , so our resulting set is the empty set.

Image of Timescale

🚀 pgai Vectorizer: SQLAlchemy and LiteLLM Make Vector Search Simple

We built pgai Vectorizer to simplify embedding management for AI applications—without needing a separate database or complex infrastructure. Since launch, developers have created over 3,000 vectorizers on Timescale Cloud, with many more self-hosted.

Read full post →

Top comments (0)

Image of Docusign

🛠️ Bring your solution into Docusign. Reach over 1.6M customers.

Docusign is now extensible. Overcome challenges with disconnected products and inaccessible data by bringing your solutions into Docusign and publishing to 1.6M customers in the App Center.

Learn more