## On the congruence of sets and their equivalence by finite decomposition |

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### Contents

Congruence of sets | 1 |

Translation of sets | 10 |

Equivalence of sets by finite | 24 |

Copyright | |

7 other sections not shown

### Common terms and phrases

absolutely measurable according aggregate aid of Zermelo's angle axis Banach's measure bers common point congruence of sets continuum decom decomposed deduced denote the set disjoint sets distance distinct points easily seen enumerable set equal equivalent by decomposition equivalent by finite Euclidean space evidently exists a plane exists a set factor family F family f>(E finite decomposition finite number formulae Fund hence hypothesis implies induction infinite sequence infinite sets interval irrational number Lebesgue sense lemma length Let us suppose linear distinct sets linear set Math measure zero metric space natural number numbers x obtained paradoxical decomposition plane set positive integer positive number Proof proper subsets proved rational numbers reciprocal univocal rotation segment set H set situated sets of points Sierpinski solid sphere square straight line superposable by translation theorem 14 theorem 23 tion transcendental number triangle whence Zermelo's axiom