I have to create a bijection between two sets - a set of rational numbers, and - a set of positive rational numbers, to show that these sets have equal cardinality.
Can anyone give me a hint?
Both in this question and the other you posted, it seems to me as if someone is asking you "to reinvent the wheel". You already have the Cantor-Bernstein' theorem.
Think about the mapping , .
Is that an injection?
In this new problem, you know that subsets of countable sets are countable.
There us a bijection as well as a bijection