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I'm trying to prove that the theory of dense linear orders and the theory of discrete linear orders are incompatible by showing that their union is inconsistent. Does anyone know how to do this? Thank you for your time

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HINT: The axioms of a dense linear order say that between any two distinct elements there is a third; what do the axioms of a discrete linear order say?

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  • $\begingroup$ Oh wow, that's incredibly simple. Thank you! $\endgroup$
    – user84815
    Jul 5 '13 at 22:08
  • $\begingroup$ @user84815: You’re welcome! $\endgroup$ Jul 5 '13 at 22:11

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