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What is the cartesian product ?
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The cartesian product $A \times B$ of sets $A$ and $B$ is the set of ordered pairs whose first component is from $A$ and the second component is from $B$. For example, if $A=\{1,2,3,4\}$ and $B=\{3, a, 9\}$, then their cartesian product is:
$A \times B=\{(1,3),(1, a),(1,9),(2,3),(2, a),(2,9),(3,3), ...$

$... (3, a),(3,9),(4,3),(4, a),(4,9)\} .$
We use the notation $A^2$ for $A \times A$.
Cartesian product is used to formally define many important concepts in mathematics. For the beginning, you may notice that we can define the two-dimensional plane as the product of the line $\mathbb{R}$ with itself. Later on we will see that relations, functions, and graphs can be defined using cartesian product.
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