]>
Prove that all the rational numbers r in the interval: are countable! Give the first 12 of them. (hint: Fig. Countability)
If we follow Fig. Countability for positive numbers, add the zero and do not count the numbers bigger than 1 , we obtain:
A different and simpler approach will be: after the zero and 1, to arrange the positive numbers smaller than 1 in groups of denominators in an increasing order (2, 3, 4, ...), while each group of the same denominator contains terms with the appropriate numerators in an increasing order. One obtains:
For any arrangement of the numbers r if there are not any missising from the interval your credit is 10.
If there are no missing numbers, but just 0 or/and 1 there your score is 5.
Otherwise your score is zero