Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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A PowerSet is a construct derived from another existing set S. Given a set S, the PowerSet of S, written P(S), is the set of all subsets of S. The definition of a subset is as follows: Given sets S and T, then T is defined to be a subset of S if every element of T is also an element of S. If S is the set {A, B, C} then {A,C} is a subset of S. There are sets that are also subset of S as well, the complete list is as follows: * {} * {A} * {B} * {C} * {A, B} * {A, C} * {B, C} * {A, B, C} So the PowerSet of S, written P(S), is the set containing all the subsets above. Written out this would be the set: P(S) = { {}, {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C} } In case you were wondering, for any given set S, S is always considered to be a subset of itself (by definition) - albeit not a ProperSubset. Also, the empty set, written {}, is also a subset of any given set S. This is because the empty set vaccuously satisfies the definition of a subset of S; since the empty set has no elements, every element it the empty set is also an element of S, for any given set S. If the above paragraph sounds a bit like double-speak - it is only because it is stating the obvious.