A sequence x_n in a metric space with metric d is convergent to a point x^* , denoted as x_n \rightarrow x^* , if for every \epsilon > 0 there is a natural number N such that for every k \ge N : d(x_k, x^*)
the rational number obtained when a continued fraction has been terminated after a finite number of terms
approaching a value For example, if you look at unit fractions (fractions with a numerator of 1), you can build a set of numbers {1/1, ½, 1/3, ¼, 1/5, ...} As the denominators get bigger, the fractions get smaller, but they are always bigger than 0 We could say that the set of unit fractions is convergent or that the set of unit fractions converges to 0