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  "body": "\n## Statement\n\nAn atom of a [[Boolean algebra|06GKBTAA5E]] $B$ is a minimal element of $B \\setminus \\{0\\}$.\nLet $B$ be a finite Boolean algebra, and let $\\operatorname{At}(B)$ be its set of atoms.\nThen the map $b \\mapsto \\{ x \\in \\operatorname{At}(B) : x \\le b \\}$ is an isomorphism from $B$ to the [[power set Boolean algebra|004J7ZEFAT]] of $\\operatorname{At}(B)$.\n\n## Remarks\n\nA consequence: a finite Boolean algebra with $n$ atoms has $2^n$ elements.\nThe general theorem says that every Boolean algebra is isomorphic to the algebra of clopen subsets of its Stone space. For a finite Boolean algebra this space is finite and discrete, and its points correspond to the atoms.\nThe general theorem needs a weak form of the axiom of choice, but the finite case does not.\n\n## History\n\nMarshall Stone published the representation theorem for all Boolean algebras in 1936.\n\n## Explanations\n\n### L1 human\n\nEach finite Boolean algebra is the algebra of all subsets of some finite set.\nEach element is the set of atoms below it, and the atoms are the smallest nonzero elements.\n",
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