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  "body": "\n## Summary\n\nLet $(x_i)_{i \\in I}$ be a family indexed by an arbitrary set $I$.\nIt is summable when its finite partial sums approach a limit as the finite set of indices grows.\nThis notion of sum uses no order on $I$, so it works for index sets such as $\\N \\times \\N$, $\\Z$ or uncountable sets.\nFor real or complex terms indexed by $\\N$, summability is the same as [[absolute convergence|0YBDSJARWN]].\nThe exact definition is in [[summable family|Z4H7272S9S]].\n\n## Explanations\n\n### L1 human\n\nAn ordinary series adds its terms in a fixed order.\nA summable family has a sum that does not depend on any order.\nOnce a large enough finite batch of terms is added, adding further terms keeps you close to the sum.\nFor example, the numbers $1/(2^m 3^n)$ for all pairs $(m, n)$ of natural numbers form a summable family with sum $3$.\n",
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