Let $A = \{ p_{i},p_{i+1},\ldots,p_{n}\}$ be any finite set of prime numbers, where $i,n \in \mathbb{N}$. And $p_{i}\in A$, is the $i$th prime number i.e. $p_{2} = 3$.
Let all possible finite sets A, that can be formed, be element of set B.
The question is, prove or disprove that there exist a bijective function $f:B\rightarrow\mathbb{N}$ such that $f(A) =p_{i}\times p_{i+1}\times\cdots\times p_{n}$
for example $f(A) = 4$ does not satisfy, because it should be $A=\{p_2,p_2\}$ which contains same element twice, and this means that cardinality of set $B$ is not $\aleph_0$ (no bijection with $\mathbb{N}$). But in a book, author uses this argument to prove that "set of all finite subsets of natural numbers, is countably infinite"