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I was reading Spivak's calculus. It starts with discussing the familiar axioms of the real numbers. He calls them properties. At some another forum, I came across the reference to Landau's "Foundation of Analysis" as a background for analysis. So I referred to that book. On the very first page , he says that reflexive, symmetric, and transitive properties of the natural numbers are taken for granted on logical grounds. So Landau is taking reflexive, symmetric and transitive properties as axioms of natural numbers. I was wondering if we can prove reflexive, symmetric and transitive properties from the field axioms given in Spivak's calculus book.

thanks

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# Proving reflexive, symmetric, transitive properties

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