## Retracing Elementary Mathematics |

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### Contents

Preface | 1 |

An Axiomatic Development of the Positive integers | 21 |

Models and Isomorphisms | 51 |

Copyright | |

37 other sections not shown

### Common terms and phrases

andy applied to lines associative law Axiom P4 Axiom Schema axiomatic theory binary operation binary relation Chapter commutative law concept Deduction Theorem applied define Definition dense ordered system element of G equation exactly x elements example Exercise extension following theorem given Hence holds induction model integral domain intuitive intuitive knowledge isomorphism Law of Addition law of logic least upper bound Lemma Let G Let x,y line 12 lines 9 logic from line mathematics multiplication nonempty notation null element null set number system object obtain one-one mapping ordered pairs Peano models positive integers proof of Theorem properties Prove Theorem rational numbers reader real numbers Right Cancellation Law Section sentence set G set H set theory solution statement Suppose symbols Theorem to lines Trichotomy Law x t G x t H x-sequence x,y e x,y t z t G