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Math and science::Analysis::Tao::06. Limits of sequences

Convergence of sequences of reals

Let \( L \) be a real number. A sequence of reals \( (a_n)_{n=m}^{\infty} \) is said to converge to \( L \) if for every real \( \varepsilon > 0 \) there exists an integer \( N \ge m \) such that [...] for all \( k \ge N \).