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  "body": "\n## Summary\n\nA complete Boolean algebra is a [[Boolean algebra|0XADJKM699]] in which every subset has a supremum, so that it is also a [[complete lattice|D7A0ZGZT5S]].\nPower sets are complete, and so are the algebras of [[regular open sets|833XAA2Q65]] of topological spaces.\nEvery Boolean algebra embeds densely into a complete one, its completion.\nComplete Boolean algebras are the basic tool of Boolean-valued models and of forcing in set theory.\n\n## Explanations\n\n### L1 human\n\nIn a Boolean algebra one can always take \"or\" of two or of finitely many elements.\nIn a complete Boolean algebra one can also take \"or\" of infinitely many elements at once, and the result is still in the algebra.\nThe subsets of a set form such an algebra: the \"or\" of any family of subsets is their union.\nThe finite and cofinite subsets of $\\N$ do not.\nThe set of even numbers is a union of finite sets, but it is neither finite nor cofinite, and the family has no least upper bound in the algebra.\n",
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