## Abstract set theory |

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### Contents

Preface | 1 |

Examples Cantors Set Concept | 11 |

Fundamental Concepts Finite and Infinite Sets | 23 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

abstract according addition alephs algebraic numbers Annalen arbitrary member arithmetic associative law axiom of choice belongs called Cantor Cartesian product concept contains continuum decimal Dedekind defined Definition denoted dense set dense-in-itself denumerable set digits disjoint sets ensembles equal equation equipollent example exists factors finite cardinals finite number finite sets formulation Foundations function gamma-set given Hausdorff hence ibid implies inequality infinite sets infinity initial instance intersection interval introduced last member Leipzig logical magnitude Math mathematical induction means Mengenlehre method multiplication null-set obtain order-types ordered pairs ordered sets ordered sum ordinal numbers pairwise disjoint particular plain sets positive integers power-set problem proof of Theorem proper subset properties prove rationals real numbers relation respect sequence set theory sets of points Sierpinski similar mapping statement Tarski transcendental numbers transfinite cardinals transfinite induction types union uniquely unit-set well-ordered set well-ordering theorem yields Zermelo