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  "body": "\n## Summary\n\nA [[summation method|8X25Q4XYMN]] is linear when it respects sums and scalar multiples of series.\nIt is stable when deleting or adding a first term changes the sum by that term.\nThese two properties, together with [[regularity|29C7C41A52]], are the ones usually expected of a reasonable method.\nThey are strong enough to force values: any linear and stable method that sums $1 - 1 + 1 - \\cdots$ must give it the value $\\frac12$.\n\n## Explanations\n\n### L1 human\n\nOrdinary sums obey two familiar rules: the sum of two series is the sum of their sums, and $a_0 + a_1 + a_2 + \\cdots$ equals $a_0$ plus the sum of the rest.\nLinear and stable methods keep these rules for the new, generalized sums.\nFor $x = 1 - 1 + 1 - \\cdots$ these rules give $x = 1 - x$, so $x = \\frac12$.\nFor $1 + 1 + 1 + \\cdots$ they would give $x = 1 + x$, which is impossible, so no such method sums this series to a finite number.\n",
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