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Sequence**

Given a set \(X\) (which may additionally be a topological space or metric space or some other structure with an underlying set), a sequence in \(X\) is just a function \(a:\mathbb{N}\to X, n\mapsto a_n\). It is common to denote a sequence by its terms, \((a_i)_{i=0}^\infty\), instead of refering to the function itself.