{
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  "body": "\n## Summary\n\nIn discrete geometry, a $k$-set of a finite point set $S$ in the [[Euclidean plane|0XW7V9ZZ05]] is a [[subset|0BJR9QR08E]] of $k$ elements of $S$ that can be strictly separated from the remaining points by a [[line|0MP9BCF6DP]]. More generally, in [[Euclidean space|0XPR1E85W0]] of higher dimensions, a $k$-set of a finite point set is a subset of $k$ elements that can be separated from the remaining points by a hyperplane. In particular, when $k=n/2$ (where $n$ is the size of $S$), the line or hyperplane that separates a $k$-set from the rest of $S$ is a **halving line** or **halving plane**.\n",
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