## The concept of number: from quaternions to monads and topological fields |

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### Contents

THE COMPLETE ORDERED FIELD R | 1 |

CONSTRUCTIONS OF R | 39 |

IRRATIONAL NUMBERS | 59 |

Copyright | |

10 other sections not shown

### Common terms and phrases

accumulation point addition algebraic numbers already Archimedean axiom basis bijection calculation Cantor cardinal numbers Cauchy functional equation Cauchy sequence Cofin commutative complete complex numbers concept consider construction Continued Fraction converges countable decimal expansion Dedekind define definition denote equation equipotent equivalent example Exercise exists filter finite formula Geometry given Hamilton Hence homomorphism infinite set infinitesimal injective injective function Intermediate Assertion intuitive inverse irrational number isomorphic least upper bound linear linearly locally compact mapping Mathematics matrices modulus multiplicative group natural numbers non-standard analysis number system obtain open sets ordered field polynomial proof properties prove pure quaternions quaternions rational numbers real numbers ring rotation scalar Section subset Suppose surjective theory topological field topological group topological space ultrafilter vector space write zero Zorn's lemma