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  "body": "\n## Summary\n\nThe sumset $A + B$ of two subsets of an abelian group is the set of all sums $a + b$ with $a \\in A$ and $b \\in B$.\nIt is the basic object of [[additive combinatorics|3NM362A2JG]].\nComparing $\\abs{A + B}$ with $\\abs{A}$ and $\\abs{B}$ measures how much additive structure the sets have.\nFor subsets of a vector space the same operation is called Minkowski addition.\n\n## Explanations\n\n### L1 human\n\nTake two sets of numbers and write down every sum of one number from the first set and one from the second.\nThe collection of these sums is the sumset.\nFor example, $\\set{0, 1} + \\set{0, 10} = \\set{0, 1, 10, 11}$.\nSets that are evenly spaced have few different sums, while scattered sets have many.\n",
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