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×E is a notation used in mathematics to indicate the Cartesian product with a set E. It is not a standalone constant or a single operation by itself. When paired with a set A, the expression A × E denotes the set of all ordered pairs (a, e) where a ∈ A and e ∈ E. The symbol × is read “times” or “cross,” and in this context it identifies a product of sets rather than the multiplication of elements.

This notation should not be confused with the vector cross product, which also uses the × symbol but denotes a different operation defined on vectors in three-dimensional space, with properties such as bilinearity and a magnitude related to the parallelogram spanned by the vectors. The Cartesian product forms a new set; it does not operate on elements of A or E.

If A and E are finite, the size of their Cartesian product is the product of their sizes: |A × E| = |A| · |E|. Beyond basic set theory, A × E is fundamental in defining product spaces in topology and in constructing product measures or product types in computer science and data modeling. It is versatile for expressing combinations of elements from two domains while preserving the order of the pair.

In practice, A × E is often used whenever a structured pairing of elements from two groups, spaces, or data domains is required, with E frequently singled out as a fixed or distinguished component.