What is the Cartesian Product of Sets? | Set Theory

What is the Cartesian product of two sets? The Cartesian product can be generalized to more than two sets, but in this video we go over Cartesian products of two sets! Here is how it works. If you have two sets, A and B, then their Cartesian product, written A x B, is the set containing all ordered pairs (a, b) where a is in A and b is in B. For example, {1, 2, 3} x {x, y, z} = { (1, x), (1, y), (1, z), (2, x), (2, y), (2, z), (3, x), (3, y), (3, z) }. Notice that the cardinality of A x B is equal to the product of the cardinalities of A and B. That is, |A x B| = |A| * |B|. This is always true.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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