The previous discussion shows, for the case "x" = 0, that one may approximate "x" to higher and higher degrees of accuracy by defining ε to be smaller and smaller. In particular, sets of the form (-ε, ε) give us a lot of information about points close to "x" = 0. Thus, rather than speaking of a concrete Euclidean metric, one may use sets to describe points close to "x". This innovative idea has far-reaching consequences; in particular, by defining different collections of sets containing 0 (distinct from the sets (-ε, ε)), one may find different results regarding the distance between 0 and other real numbers. For example, if we were to define R as the only such set for "measuring distance", all points are close to 0 since there is only one possible degree of accuracy one may achieve in approximating 0: being a member of R. Thus, we find that in some sense, every real number is distance 0 away from 0. It may help in this case to think of the measure as being a binary condition: all things in R are equally close to 0, while any item that is not in R is not close to 0.