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Math and science::Analysis::Tao::05. The real numbers

ε-close sequences

Let \( (a_n)_{n=0}^{\infty} \) and \( (b_n)_{n=0}^{\infty} \) be two sequences and let \( \varepsilon > 0 \) be a rational. \( (a_n)_{n=0}^{\infty} \) is said to be ε-close to \( (b_n)_{n=0}^{\infty} \) iff [...] for all \( k \ge 0 \).