2.1: Convergence - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Analysis/Introduction_to_Mathematical_Analysis_I_(Lafferriere_Lafferriere_and_Nguyen)/02%3A_Sequences/2.01%3A_Convergence
webWe say that the sequence {an} converges to a ∈ R if, for any ε > 0, there exists a positive integer N such that for any n ∈ N with n ≥ N, one has. |an − a| < ε( or equivalently , a − ε < an < a + ε). In this case, we call a the limit of the sequence (see Theorem 2.1.3 below) and write limn → ∞an = a.
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