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  "body": "\n## Summary\n\nA double sequence is a family $(x_{m,n})$ indexed by pairs of natural numbers, like an infinite matrix.\nIt has several notions of limit.\nThere is the joint limit as $m$ and $n$ both grow, and there are two iterated limits taken one index at a time.\nThese limits can differ, and theorems such as the [[Moore–Osgood theorem|QN2210XCST]] say when they agree.\nThe exact definition is in [[double sequence|WK5V372TG3]].\n\n## Explanations\n\n### L1 human\n\nA double sequence is an infinite table of numbers with rows and columns, one entry for each pair $(m, n)$.\nFor example, $x_{m,n} = m + n$ gives the table with rows $0, 1, 2, \\ldots$ and $1, 2, 3, \\ldots$ and so on.\nOne can let the row number grow first, or the column number first, or both together, and the outcomes need not be the same.\n",
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