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  "body": "\n## Definition\n\nLet $X$ be a set and let $a, b \\in X$ with $a \\neq b$.\nThe transposition $(a\\ b)$ is the permutation of $X$ that sends $a$ to $b$, sends $b$ to $a$, and fixes each other element of $X$.\n\n## Remarks\n\nA transposition is a $2$-cycle in [[cycle notation|0ZKPH2BD1T]], and $(a\\ b) = (b\\ a)$.\nEach transposition is its own inverse, so it has [[order|0WE2NHZJ7B]] $2$.\nThe symmetric group $S_n$ contains exactly $\\binom{n}{2}$ transpositions.\n\n## Explanations\n\n### L1 human\n\nA transposition swaps two things and leaves everything else in place.\nIf you do the same swap two times, you are back at the start.\nAll permutations can be built from transpositions.\n",
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