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  "body": "\n## Definition\n\nLet $A$ and $B$ be [[sets|0SJ3RX9TXA]].\nThe Cartesian product of $A$ and $B$ is the set\n$$A \\times B = \\{(a, b) \\mid a \\in A \\text{ and } b \\in B\\}$$\nof all [[ordered pairs|0JQWWFCS9R]] $(a, b)$ with $a \\in A$ and $b \\in B$.\n\n## Remarks\n\nExample: $\\{1, 2\\} \\times \\{x, y\\} = \\{(1, x), (1, y), (2, x), (2, y)\\}$.\nFor finite sets with $m$ and $n$ elements, $A \\times B$ has $mn$ elements.\nThe plane $\\mathbb{R}^2$ is $\\mathbb{R} \\times \\mathbb{R}$.\nA [[binary relation|08EJC6Q25H]] from $A$ to $B$ is a subset of $A \\times B$.\n\n## Explanations\n\n### L1 human\n\nThink of a table with a row for each element of $A$ and a column for each element of $B$.\nEach cell of the table is one pair $(a, b)$.\nThe Cartesian product is the set of all the cells.\n",
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