Proof of ΦxΦ = Φ and the special case of \emptyset\times\emptyset =\emptyset

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The discussion centers on proving that the Cartesian product of the empty set with itself equals the empty set, expressed as ∅ × ∅ = ∅. Participants argue over the validity of different proof methods, including direct proofs and proofs by contradiction. Some assert that the empty set's definition inherently supports the conclusion, while others challenge the rigor of informal proofs. The conversation highlights the importance of formal proofs in mathematics, with some participants advocating for clarity and explicitness in proof presentation. Ultimately, the consensus leans towards recognizing the validity of the proof while debating the necessity of formalism in mathematical arguments.
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There is another PF member, poutsos.A, with the exact same prose as evagelos. They usually mutually agree on each other's posts. I wonder...
 

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