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  "body": "\n## Definition\n\nLet $\\sum_{n=0}^{\\infty} a_n$ be a real [[series|0JH4MN4K1C]].\nLet $\\sigma \\colon \\mathbb{N} \\to \\mathbb{N}$ be a bijection.\nThe series $\\sum_{n=0}^{\\infty} a_{\\sigma(n)}$ is a rearrangement of $\\sum a_n$.\n\n## Remarks\n\nA rearrangement uses each term of the original series exactly once, in a new order.\n[[Rearrangements of an absolutely convergent series have the same sum|0J76TP9FGD]].\nFor a [[conditionally convergent|02YRQXZDCS]] series, rearrangements can change the sum, by the [[Riemann rearrangement theorem|0E7VBYGFF7]].\n\n## Explanations\n\n### L1 human\n\nA rearrangement adds up the same terms in a different order.\nFor finite sums the order does not matter, but for infinite series it can matter.\n",
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