TheoremBase

Cartesian Product of Two Sets, via Ordered Pairs

Statement

Let XX and YY be sets, and let (x,y)(x,y) denote the ordered pair of xx and yy.

The Cartesian product of XX and YY is the set

X×Y={ p : p=(x,y) for some x∈X and some y∈Y }.X\times Y=\bigl\{\,p\ :\ p=(x,y)\ \text{for some }x\in X\text{ and some }y\in Y\,\bigr\}.

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