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

Limits of sequences

If a sequence of reals \( (a_n)_{n=m}^{\infty} \) converges to a real \( L \), we say that \( (a_n)_{n=m}^{\infty} \) is [...] and that \( L \) is the [...]. We write:
\[ L = \lim_{n\to\infty}a_n \]

If a sequence does not converge to a real, then it is said to [...] or be [...]. \( \lim_{n\to\infty}a_n \) is left undefined for a divergent sequence.