I have begun some studying of set theory at a level which could be described as "undergraduate level".
So there is some definition of cardinality and bijections between $\mathbb N$ and $\mathbb Q$, and uncountability of $\mathbb R$ and countability of $\mathbb N$ and $\mathbb Q$.
So, it is really a beginning of some possible further study, with just some basic concepts that I have grasped so far.
But, it seems legal to ask at this level, is there a bijection between the set of all countable subsets of $\mathbb I$ and $\mathbb R$?
Here $\mathbb I$ denotes the set of all irrational numbers, and if $\mathbb I_C$ denotes the set of all countable subsets of $\mathbb I$, this question is: Is there a bijection $b: \mathbb I_C \to \mathbb R$?
I would also like to see a constructed example of such bijection.