## In search of infinity |

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### Contents

The mysteries of infinite sets | 33 |

Remarkable functions and curves or a stroll | 71 |

In search of the absolute | 117 |

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### Common terms and phrases

19th century actual infinite ancient Greek angle sum angular excess areas of mathematics axiom of choice Borel Cantor cardinality compute concept construct continuum hypothesis contradictions cosmic zoologists countable set curvature of space curve defined definition digit dimension Ekslings enumerate equations example existence finite sets French mathematician galaxies Gaussian curvature geometric figures geometry German mathematician hall of wonders Hilbert idea infinite sets infinity integers intuition Jordan Lebesgue Lebesgue integral length Luzin magnitudes mathematical analysis mathematical hall mathematician maxima and minima measure natural numbers notion number theory obtained one-to-one correspondence paradoxes parallel transport physicist plane problem proof properties prove question rational numbers real numbers result rigorous scholars sequence set of natural set of points set theory set-theoretic Soviet mathematician sphere square straight line subset surface theorems theory of functions theory of infinite transfinite numbers triangle turned uncountable uncountable set Universe Urysohn Zeno's Zeno's paradoxes zero