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  "body": "\n## Summary\n\nA series converges unconditionally when every reordering of its terms still converges.\nFor real or complex series this is the same as [[absolute convergence|0YBDSJARWN]], by the [[Riemann rearrangement theorem|0E7VBYGFF7]].\nIn infinite-dimensional Banach spaces the two notions differ, and unconditional convergence is the natural notion for sums without a preferred order.\nThe exact definition is in [[unconditional convergence|GA7Q813F50]].\n\n## Explanations\n\n### L1 human\n\nSome infinite sums give different answers when you add the terms in a different order.\nAn unconditionally convergent series is one where the order never matters: every order converges, to the same sum.\nFor example $1 + \\tfrac14 + \\tfrac19 + \\cdots$ converges in any order, while $1 - \\tfrac12 + \\tfrac13 - \\cdots$ can be reordered to converge to any real number.\n",
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