## Uses of InfinityThis intriguing, accessible work leads readers to an excellent grasp of the fundamental notions of infinity used in the calculus and in virtually all other mathematical disciplines. Designed to make minimal demands on readers' mathematical abilities, this perceptive volume employs an intuitive and descriptive approach that will appeal to students, teachers, and the mathematically inclined. Each chapter's teachings are supplemented by challenging problems, with solutions at the end of the book. 83 text figures. 1962 edition. |

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### Contents

Preface | 3 |

Popular and Mathematical Infinities | 25 |

From 2 to the Transfinite | 38 |

To the Limit if the Limit Ezists | 59 |

The Self Perpetuating Golden Rectangle | 75 |

Constructions and Proofs | 96 |

Solutions to Problems | 121 |

150 | |

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### Common terms and phrases

angle approaches zero assertion Bolzano-Weierstrass theorem C. D. Olds calculate called Chapter consecutive construction countable set curve defined definition denote diagonal digits distance divided equal equation example exceeds fact Fibonacci numbers Fibonacci sequence Figure finite number formula fraction geometric given golden ratio golden rectangle harmonic series Hence illustrations increases inductive step infinite process infinite sequence infinite set integers irrational larger length letters limit exists limit point logarithmic spiral logarithms mathematical induction mathematicians method mod JV modulo natural numbers number of terms ordinate pair perpendicular photographs plane points PI positional notation positive Problem prove quadratrix quarter-turns radians rational numbers reader reciprocal recursion residues mod ruler segment sequence of numbers sequence of points sequence of residues side smaller special rectangles spiral square Suppose tion triangle uncountable set vertices whole numbers zig-zag