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The notation $\{ x_1,x_2,x_3,\ldots,x_n \}$ means "the set of elements $x_1,x_2,x_3,\ldots,x_n$". In particular, all elements in the set are listed. If an element isn't listed, it doesn't belong to the set. For example, $\epsilon$ is not an element of $\{ab,b\}$. There is absolutely nothing special about $\epsilon$. It is a bona fide word, and ...


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