I need to find and prove an if and only if condition for:
$A_1\times A_2 \times A_3 \times \cdots $
Being a countable set, given that for all $i$ $A_i \subseteq \mathbb N$
Any tips on what the condition could be?
(For countability in this case it is meant there is a bijection from naturals to the set, or that it is finite).