Basic Set Theory

Basic Set Theory

For each i $$\in$$ N, let $$f_{i }$$ : N $$\rightarrow$$ {0, 1}. Let B = {$$f_{i }$$ : i ∈ N} and
E = {n ∈ N : $$f_{n }$$(n) = 0}.
Does there exist a f ∈ B such that E = {n ∈ N : f(n) = 1} ? Justified.
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