In the set of all real numbers, one has the natural Euclidean metric; that is, a function which measures the distance between two real numbers: . Therefore, given a real number "x", one can speak of the set of all points close to that real number; that is, within ε of "x". In essence, points within ε of "x" approximate "x" to an accuracy of degree ε. Note that ε > 0 always but as ε becomes smaller and smaller, one obtains points that approximate "x" to a higher and higher degree of accuracy. For example, if "x" = 0 and ε = 1, the points within ε of "x" are precisely the points of the interval (-1, 1); that is, the set of all real numbers between -1 and 1. However, with ε = 0.5, the points within ε of "x" are precisely the points of (-0.5, 0.5). Clearly, these points approximate "x" to a greater degree of accuracy than when ε = 1.