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My professor mentioned the below statement in class but without a proof. I am trying to prove it for myself as I don't understand 100% why this is always the case. Given is A, a subset of {0,1}$^*$.

ε $\in\ A^+$ <-> ε $\in\ A$, where ε is the empty word. I thought of doing a proof by contradiction to show -> by assuming the empty word is not part of A$^+$.

Any help is much appreciated!

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