## Elementary Set Theory, Part I/IIThis book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory. |

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This is a very basic, fundamental book on set theory.

It describes all the necessary concepts that are essential to construct a set and It is free from conceptual loop holes at my level of understanding .

### Contents

3 | |

SETS | 22 |

CHAPTERS RELATIONS | 43 |

MAPPINGS | 53 |

FAMILIES | 67 |

NATURAL NUMBERS | 77 |

FINITE AND INFINITE SETS | 91 |

ORDERED SETS | 102 |

ORDINAL NUMBERS AND CARDINAL NUMBERS | 117 |

SPECIAL SYMBOLS AND ABBREVIATIONS | 129 |

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### Common terms and phrases

A U B axiom of choice axiom of extension belongs bijective mapping called cardinal cartesian product concept construct definition denote disjunction empty family empty set equal equipotent equivalence relation example exists F F F F T F family of elements family of sets family of subsets finite sets following conditions following theorem hence Hong Kong inclusion infinite set injective integers intersection isomorphic iterated composition least element mathematical induction maximal element natural numbers natural sequence negation non-empty set number of elements objects ordered pair ordered set ordinal numbers power set PROOF proper segment proper subset Prove quotient set rational numbers recursion theorem respectively Section set of departure set theory singleton statement function successor set surjective symbol topology transfinite induction true truth functional truth table truth value ty(A union usual order relation valid formula well-ordered set well-ordering principle