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  "body": "\n## Summary\n\nAn approximately additive function is a map $f$ from an abelian group to a normed space.\nThe norm of its defect $f(x + y) - f(x) - f(y)$ is at most a fixed $\\delta$.\nIt is an [[additive function|KF719SZD5T]] up to a uniform error.\n[[Hyers' theorem|VFRJ0P2P15]] says that an approximately additive map from a normed space to a Banach space lies within $\\delta$ of a unique additive map.\nSuch maps are also called $\\delta$-additive maps.\n\n## Explanations\n\n### L1 human\n\nAn additive function turns sums into sums exactly.\nAn approximately additive function does so with an error that never exceeds a fixed amount.\nThe floor function is an example: $\\floor{x + y} - \\floor{x} - \\floor{y}$ is always $0$ or $1$.\nIt stays within distance $1$ of the additive function $x \\mapsto x$.\n",
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