Hello(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proving reflexive, symmetric, transitive properties

Loading...

Similar Threads - Proving reflexive symmetric | Date |
---|---|

I A problematic limit to prove | Jan 26, 2018 |

I Proving equivalence between statements about a sequence | Feb 12, 2017 |

I Prove that ∫f(x)δ(x)dx=f(0) | Jan 22, 2017 |

I Prove ln(x) <= x-1 for positive x | Jan 15, 2017 |

Why is [tex]l^1[/tex] not reflexive | Apr 12, 2005 |

**Physics Forums - The Fusion of Science and Community**