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  "body": "\n## Definition\n\nAn ordered pair $(a, b)$ has a first entry $a$ and a second entry $b$, with this property:\n$$(a, b) = (c, d) \\iff a = c \\text{ and } b = d.$$\nIn set theory, the Kuratowski definition is $(a, b) = \\{\\{a\\}, \\{a, b\\}\\}$. It has the property above.\n\n## Remarks\n\nIn general $(a, b) \\neq (b, a)$, but the sets $\\{a, b\\}$ and $\\{b, a\\}$ are equal.\nOrdered pairs are the elements of a [[Cartesian product|0C81YBVTWH]].\nAn ordered triple can be defined as $(a, b, c) = ((a, b), c)$.\n\n## Explanations\n\n### L1 human\n\nA point in the plane is an ordered pair of coordinates.\nThe points $(1, 2)$ and $(2, 1)$ are different, so the order matters.\nThe Kuratowski definition only shows that sets can model pairs.\n",
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