 This charge can be dispelled by a closer look at the definition of a limit, which shows that infinite limits in fact have important implications for the dynamical behaviour of the system in finite times. The definition of a limit is as follows (where \(f\) is an arbitrary function of time): lim\(_{t\rightarrow \infty} f(t) = c\) iff for every \(\varepsilon \gt 0\) there exists an \(t’ \gt 0\) so that for all \(t \gt t’\) we have \(\lvert f(t) - c\rvert \lt \varepsilon\). In words, for every number \(\varepsilon\), no matter how small, there is a finite time \(t’\) after which the values of \(f\) differ from \(c\) by less then \(\varepsilon\). That is, once we are past \(t’\) the values of \(f\) never move more than \(\varepsilon\) away from \(c\). With this in mind strong mixing, for instance, says that for a given threshold \(\varepsilon\) there exists a finite time \(t_n (n\) units of time after the current time) after which \(C(T_n B, A)\) is always smaller than \(\varepsilon\). We are free to choose \(\varepsilon\) to be an empirically relevant margin, and so we know that if a system is mixing, we should expect the correlations between the states of the system after t\(_n\) and its current state to be below \(\varepsilon\). The upshot is that in strong mixing systems, being in a state \(B\) at some past time becomes increasingly irrelevant for its probability of being in the state \(A\) now, as the temporal distance between \(A\) and \(B\) becomes larger. Thus, the fact that system is strong mixing clearly has implications for its dynamical behaviour in finite times. Furthermore, often (although not always) convergence proofs provide effective bounds on rates of convergence and these bounds can be used to inform expectations about behaviour at a given time.