Understanding of countable set short theorem. I am struggling to understand what the theorem is stating. 

Question 1
Let n equals 2, would that mean that $B_n$ would be $B_2$= $\left\{\left\{a_1\right\},\left\{a_1,a_2\right\}\right\}$?
Question 2
Given n=2 and 3 how would small b, be described? 
In the case of $B_{n-1}$,would the sets (b,a), be
(0,$a_1$),($b_1$,$a_2$).
I have a feeling I am totally lost and I am hoping someone could provide a descret example so that I understand what it is stating?

Question 1: If $n=2$ then $B$ is of the form $B_2 = \{ (a_i , a_j) : a_i , a_j \in A\}$. 
Question 2: n - 1 = 2 , n = 3 
$ \{ (b , a) : b \in B_2  , a \in A \}$ It is like $( (a_i , a_j ) , a_k) $ and $a_i , a_j , a_k \in A$.
