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  "body": "\n## Definition\n\nLet $A$ be a set and let $n$ be a natural number.\nThe set $A$ has $n$ elements if there is a bijection from $\\{1, 2, \\dots, n\\}$ to $A$.\nFor $n = 0$, the set $\\{1, \\dots, n\\}$ is the empty set, so only the empty set has $0$ elements.\nA set is finite if it has $n$ elements for some natural number $n$.\n\nFor a finite set $A$, this number $n$ is unique.\nIt is the cardinality of $A$, with the notation $|A|$ or $\\# A$.\n\n## Remarks\n\nTwo finite sets have the same cardinality if and only if there is a bijection between them. The [[bijection principle|0GV2573FP4]] states this.\nFor example, $|\\{a, b, c\\}| = 3$ and $|\\varnothing| = 0$.\nThe uniqueness of $n$ follows from the fact that there is no injection from $\\{1, \\dots, m\\}$ to $\\{1, \\dots, n\\}$ when $m \u003e n$.\n\n## Explanations\n\n### L1 human\n\nThe cardinality of a finite set is the number of its elements.\nTo count a set, you label its elements $1, 2, 3, \\dots$ without gaps and without repeats.\nThe last label is the cardinality.\n",
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