## Abstract set theory |

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### Contents

Exponentiation of Cardinals Trans finite Numbers and Infinites | 1 |

chapter | 4 |

Fundamental Concepts Finite and Infinite Sets | 12 |

Copyright | |

13 other sections not shown

### Common terms and phrases

abstract sets addition alephs algebraic numbers Annalen argument arithmetic axiom of choice belongs called Cantor cardinal number Cartesian product concept contains continuum continuum hypothesis decimal Dedekind defined Definition denoted denumerable set digits disjoint sets equal equation equipollent equivalence theorem example exists finite cardinals finite number finite sets Foundations function gamma-set given hence Hereby ibid implies infinite sets infinity instance intersection interval introduced logical Math mathematical induction mathematicians means membership relation Mengenlehre method multiplication non-empty null-set objects obtain order-types ordered pairs ordered sets ordered sum ordinals pairwise disjoint particular Philos plain sets positive integers power-set principle problem proof of Theorem proper subset properties prove rational numbers real numbers reflexive respect segment sequence set theory Sierpinski similar mapping statement Tarski term transcendental numbers transfinite cardinals transfinite induction types union unit-set well-ordered set well-ordering theorem yields Zermelo