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  "body": "\n## Definition\n\nLet $n$ be a natural number.\nThe factorial of $n$ is the natural number $n!$ defined by the recursion\n$$0! = 1, \\qquad (n+1)! = (n+1) \\cdot n!.$$\nFor $n \\ge 1$ this gives $n! = 1 \\cdot 2 \\cdots n$, the product of the positive integers up to $n$.\n\n## Remarks\n\nThe first values are $0! = 1$, $1! = 1$, $2! = 2$, $3! = 6$, $4! = 24$ and $5! = 120$.\nThe value $n!$ is the [[number of permutations|0CEBCS0E0E]] of an $n$-element set.\nThe convention $0! = 1$ agrees with the empty product, and it makes the [[factorial formula for binomial coefficients|033KTKKRV6]] true for $k = 0$ and $k = n$.\n\n## Explanations\n\n### L1 human\n\nThe factorial $n!$ multiplies all whole numbers from $1$ to $n$.\nIt counts the ways to put $n$ different books in a row: $n$ choices for the first place, $n - 1$ for the second, and so on.\n",
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