## An Introduction to the Foundations and Fundamental Concepts of Mathematics |

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#### LibraryThing Review

User Review - divisionbyzer0 - LibraryThingThis is an excellent book tracing the history of deductive procedures and key concepts relevant to the foundation of modern mathematics, specific focus on deductive axiomatics and the utility of ... Read full review

### Contents

One MATHEMATICS BEFORE E UCLID | 5 |

Two EUCLIDS ELEMENTS | 25 |

Three NONEUCLIDEAN GEOMETRY | 52 |

Copyright | |

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### Common terms and phrases

addition and multiplication American Mathematical Monthly applied arithmetic assumed assumption Axiom of Choice binary operation Boolean algebra branch of mathematics calculus of propositions called cardinal number circle commutative complex number concept congruent consider consistent construct contains corresponding deductive deﬁned deﬁnition denote discourse dyadic relation elementary equal equation established Euclid’s Elements Euclidean geometry Euclidean tools example exists ﬁfth postulate ﬁgure ﬁnd ﬁrst ﬁve ﬁxed function given Greek Hilbert hypothesis implied inﬁnite inﬂuence integers interpretation intersect inverse Lobachevskian mathematical induction mathematical method mathematicians natural numbers non-Euclidean geometry ordered ﬁeld ordered pairs parallel postulate perpendicular points positive integers postulate set primitive terms Problem projective geometry proof properties prove quadrilateral rational numbers real number system reductio ad absurdum right angles satisﬁed Section set of postulates set theory Show signiﬁcance space statement straight line subset tautology transformations true truth table