This definition is certanly non-intuitive, so we should first check that it at least makes sense, i.e. that it always gives a unique number that can be called the distance between the two points. Notice that the cross ratio is real and positive, since , , , and are concyclic, with the pairs , and , not separating each other. This is important, since logarithms are defined only for positive reals: the formula at least produces a number. Is this number unambiguously defined? The only potential source of ambiguity is in the order of the edgepoints. But switching the two just replaces the cross ratio by its reciprocal and the logarithm by its negative: the absolute value produces the same result either way, so there is no ambiguity. Something useful to note: if and are chosen so that , , , and are in cyclic order (as in the sketch), the cross ratio is in fact greater than (check it out) and logarithm is then positive. Thus for , , , and in cyclic order, we may drop the absolute value in the distance formula.