## Abstract Set Theory |

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### Contents

Introduction | 1 |

Exponentiation of Cardinals Transfinite Numbers and Infinites | 7 |

Fundamental Concepts Finite and Infinite Sets | 13 |

Copyright | |

11 other sections not shown

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### Common terms and phrases

addition alephs algebraic numbers arbitrary member arithmetic assumption axiom of choice belongs called Cantor cardinal number Cartesian product concept contains continuum decimal Dedekind defined denoted denumerable set denumerable subset digits disjoint sets equal equation equipollent equivalence theorem example exists finite cardinals finite number finite sets Foundations fractions function gamma-set hence Ibid implies infinite sets infinity instance intersection interval introduced last member least logical Math mathematical induction means multiplication non-empty null-set objects obtain one-to-one correspondence order-types ordered pairs ordered sets ordered sum ordinals pairwise disjoint particular plain sets positive integers power-set problem proof of Theorem proper subset properties prove rational numbers real numbers reflexive remark respect segment sequence set theory sets of points similar mapping single member single-valued statement Tarski term transcendental numbers transfinite cardinals transfinite induction types union uniquely determined unit-set well-ordered set well-ordering theorem yields Zermelo