Relative abundance of rationals in Cantor's bijection? Can anybody calculate the limit of the relative abundance of rational numbers in the unit intervals (0, 1) and (1000, 1001) appearing in Cantor's famous sequence 1/1, 1/2, 2/1, 1/3, ...?
Can anybody find an interpretation for the fact that it is not 1?

Let $q_1, q_2, ...$ be the enumeration, concerning the Problem:
$$\lim\limits_{k\to\infty}\frac{|\{x ∈ \mathbb{R}| n < x \leq n+1\} ∩ \{q_1, q_2, ..., q_k\}|}{|\{x ∈ \mathbb{R} | 0 < x \leq 1\} ∩ \{q_1, q_2, ..., q_k\}|}$$
It has been conjecture that the ratio is:
$$\frac{2}{(+1)(+2)}$$
But proof is still missing.
