Denote $S = \{(a_1, a_2, a_3, \dots)| a_i \text{is 0 or 1}\}$.
So I know if I think of one S as $\{(a_1,a_2,a_3,\dots)\}$ and another S as $\{(b_1,b_2,b_3,\dots)\}$, I can create a function that spits out something like $\{(a_1,b_1, a_2,b_2, a_3, b_3, \dots)\}$. I've seen this sort of thing before when showing that (0,1)x(0,1) bijects to (0,1), but I'm having trouble proving that such a function is injective and surjective. Thanks.
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