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  "body": "\n## Summary\n\nA [[summability method|8X25Q4XYMN]] is regular when it sums every convergent sequence to its ordinary limit.\nRegularity is the basic requirement for a method to count as a generalization of convergence.\nFor matrix methods it is characterized by the [[Silverman–Toeplitz theorem|S4J7SRPXMZ]].\n\n## Explanations\n\n### L1 human\n\nA new way of summing series should not change the answer for series that already have a sum.\nRegular methods have this property: on convergent series they agree with the ordinary sum, and they only add new values for some divergent series.\nCesàro summation is regular, because the running averages of a convergent sequence tend to the same limit.\n",
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