Then arrange the rational numbers on (0, 1) according to certain rules, and set them as r 1, R2 and R3. ...

Then put 0 → r 1, 1 → R2, r 1 → R3, R2 → R4 R (n) → R (n+2).

This is a one-to-one mapping from (0, 1) to [0, 1].