## Infinity: Beyond the Beyond the Beyond"The interpolations tying mathematics into human life and thought are brilliantly clear."— "Her presentation…is conversational and humorous, and should help to simplify some complex concepts."— Infinity. It sounds simple…but is it? This elegant, accessible, and playful book artfully illuminates one of the most intriguing ideas in mathematics. Lillian Lieber presents an entertaining, yet thorough, explanation of the concept and cleverly connects mathematical reasoning to larger issues in society. "Another excellent book for the lay reader of mathematics…In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."— "Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in |

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### Contents

Dedication | 13 |

Inﬁnity in Mathematics | 27 |

More About Potential Inﬁnity | 40 |

NonEuclidean Geometries | 62 |

Actual Inﬁnity | 77 |

Actual Inﬁnity cont | 87 |

A Still Greater Actual Inﬁnity | 100 |

The Continuum of Real Numbers | 109 |

Operations on Transﬁnites 13 7 | 137 |

Higher Dimensions | 147 |

A Hierarchy of Inﬁnities | 161 |

A Brief Summary | 182 |

Is It Legitimate? | 194 |

Some Very Interesting Inﬁnite Sets | 204 |

Paradoxes in the Theory ofTransﬁnites | 240 |

The Moral | 257 |