## Introduction to abstract mathematics |

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### Contents

Logic and Set Theory | 1 |

The Natural Numbers | 55 |

The Integers and the Rational Numbers | 77 |

Copyright | |

4 other sections not shown

### Common terms and phrases

additive inverse arbitrary assume Axiom calculus called cancellation law cardinal number cardinally equivalent chapter choose closed Closure Law conclude construction continuous at x0 Corollary countable defined Definition denoted directed function endpoint equal equation equivalence classes equivalence relation example Exercise function with domain greatest common divisor Hence Hint identity implies inequality integer containing integers interior point isomorphism law for addition least upper bound Lemma limit point linear ordering mathematics means metric space multiplicative inverse N X N natural numbers neighborhood system nonempty set notation open sentence open set ordered field ordered pair partition positive integer prime Proof Let proof of Theorem properties Prove rational number reader real numbers real-valued function Riemann integral satisfying sequence set theory Show smallest Sr(x statement subintervals subset suppose Theorem 3.8 trichotomy law true unique upper number usual metric well-defined law write