The rational numbers form a countably infinite set, just as the integers do. For the integers, there is no integer between 4 and 5 (I.e., there is such a thing as two consecutive integers) So, I am thinking that there must be such a thing as two consecutive rational numbers, such that there is no other rational number that is between them. The difference between two consecutive integers is 1. If there is such a thing as two consecutive rational numbers, is the difference between them 0 (even though there are irrationals between them)?
Thanks!