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Graduate Axiom of choice: Replacing a strong condition with a weaker condition
Sorry there was a typo in (**) Corrected: (**) if A≈B & C≈D & A∩C≈B∩D then A∪C≈B∪D- jose diez
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- Forum: Set Theory, Logic, Probability, Statistics
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Graduate Axiom of choice: Replacing a strong condition with a weaker condition
This set-theory theorem is very easy to prove: (*) if A≈B & C≈D & A∩C=∅ & B∩D=∅ then A∪C≈B∪D It seems intuitive that if one replaces the strong A∩C=∅ & B∩D=∅ condition by the weaker A∩C≈B∩D the implication (**) if A≈B & C≈D & A∩C≈B∪∩D then A∪C≈BD still holds. (**) does not seem to be much...- jose diez
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- Axiom Choice
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- Forum: Set Theory, Logic, Probability, Statistics