\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)

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 \( k \ge 0 \).