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Set**

Loosely speaking, a set is a collection of elements, denoted \(a\in X\) ('\(a\) is contained in the set \(X\)'). One may denote a set by a rule which its members obey: \(X=\{a\in Y|P(a)\}\), for \(Y\) some larger set and \(P(a)\) some proposition. More formally, a set is an object which obeys a set of axioms, typically the Zermelo-Fraenkel axioms and the axiom of choice, which tell us what is and is not a set.