Basic Set Theory(Proof)

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