Just curious. Can you site a reference on this comment: Not particularly relevant; only a countable number of irrationals can appear as the limit of computations. And some pairs of rationals have no irrationals between them (for example, 0 and the nearest rational to it, which is of the form 1/x, cannot have any irrationals between them, even though (1/x and 1/(x-1)) has an countable infinity of rationals between _them_).
What are some other rational pairs which don't have any irrationals between them? I can see that given an irrational number close to zero one can generate a rational that is closer to zero. But then one can find an irrational smaller than that rational. Continue forever. The method of showing that there are as many counting numbers as rationals is by setting up a one-to-one correspondence. But the only reasoning I can think of for no irrationals to come between 0 and 1/x sounds a lot like saying one cannot reach the finish line because you have to go half-way to the finish first. What the rational (pun intended) behind this statement? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
