Happy New Year! Yes, the current one, not a previous one; this is a new post, we swear!
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LOLI'm sorry, iago, but I have noticed a major flaw in your proof.We have [tex]Ender \in A[/tex] (clearly) and [tex]Ender \in B[/tex] (since he was once a gamer in the past). Thus [tex]A \cap B \neq \emptyset[/tex]qed.