Combinatorics
A power set is the set of all possible subsets of a given set, including the empty set and the set itself. It is denoted as $$P(S)$$ or $$2^S$$ for a set $$S$$, and its size is determined by the formula $$|P(S)| = 2^{|S|}$$, where $$|S|$$ is the number of elements in the original set. The concept of power sets is crucial in combinatorics, particularly in understanding how Bell numbers enumerate partitions of sets.
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