## Set theory and logic |

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### Contents

Introduction | 1 |

Logical Problems of Finiteness and Infinity The Axiom | 26 |

Transfinite Cardinals Paradoxes of Set Theory | 41 |

Copyright | |

3 other sections not shown

### Common terms and phrases

abstract according addition aleph algebraic numbers arbitrary element argument arithmetic assigned assumption axiom of choice axiomatic method belongs Bernays called Cantor Cantor's theorem cardinal number Cartesian product choice function choice set comprehensive constructive continuum problem contradiction decimals Dedekind defined definition denote denumerable set denumerable subset disjoint distinguished element equal example exist fact factors finite cardinals finite number finite sets follows formulation Fundamental Theorem gamma set geometry given hence implies impredicable infinite set infinity instance intersection logical magnitude mapping Math mathematical induction mathematicians means Mengenlehre nature nonempty noninductive null set obtain order type ordered set ordinal pair paradoxes plain sets positive integers power set prime numbers principle procedure proof of Theorem proper subset prove real numbers relation Russell second property segment set that contains set theory sets are equivalent sets of points shows similar single element smaller statement symbolic transfinite cardinals transfinite induction union well-ordered sets well-ordering theorem Zermelo