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Set (mathematics)
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===Algebra of subsets=== {{main|Algebra of sets}} The set of all subsets of a set {{tmath|U}} is called the [[powerset]] of {{tmath|U}}, often denoted {{tmath|\mathcal P(U)}}. The powerset is an algebraic structure whose main operations are union, intersection, set difference, symmetric difference and absolute complement (complement in {{tmath|U}}). The powerset is a [[Boolean ring]] that has the symmetric difference as addition, the intersection as multiplication, the empty set as [[additive identity]], {{tmath|U}} as [[multiplicative identity]], and complement as additive inverse. The powerset is also a [[Boolean algebra (structure)|Boolean algebra]] for which the ''join'' {{tmath|\lor}} is the union {{tmath|\cup}}, the ''meet'' {{tmath|\land}} is the intersection {{tmath|\cap}}, and the negation is the set complement. As every Boolean algebra, the power set is also a [[partially ordered set]] for set inclusion. It is also a [[complete lattice]]. The axioms of these structures induce many [[identities (mathematics)|identities]] relating subsets, which are detailed in the linked articles.
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