TITLE: is it possible to count the number of rational numbers there are between any two integers?
QUESTION [5 upvotes]: im having trouble in this can anyone help me?
is it possible to count the number of rational numbers there are between any two integers?

REPLY [1 votes]: $$
\frac 1 2,\quad \underbrace{\frac 1 3, \frac 2 3}_{\bullet/3}, \quad \underbrace{\frac 1 4, \frac 3 4}_{\bullet/4}, \qquad \underbrace{\frac 1 5, \frac 2 5, \frac 3 5, \frac 4 5}_{\bullet/5}, \quad \underbrace{\frac 1 6, \frac 5 6,}_{\bullet/6} \quad\underbrace{\frac 1 7, \frac 2 7, \frac 3 7, \frac 4 7, \frac 5 7, \frac 6 7,}_{\bullet/7} \quad \underbrace{\frac 1 8, \frac 3 8, \frac 5 8, \frac 7 8,}_{\bullet/8} \quad \ldots
$$
This sequence "counts" all the rational numbers between $0$ and $1$.
{"set_name": "stack_exchange", "score": 5, "question_id": 1901711}