## Absolute Space, Absolute Time, & Absolute MotionAbsolute Space, Absolute Time, and Absolute Motion exist. These are shown to be facts through an investigation of the nature of infinitesimals. Knowledge of that nature also makes the irrational magnitudes within the unit comprehensible. The number line is shown to be cognitively superior to set theory; furthermore, non-Euclidean geometry is shown to be a mere manipulation of symbols and not an expression of a "parallel universe." Inside, the reader will also learn about a hitherto unknown number system locked within _-1. He will also discover in the infinitesimal calculus a hidden key to a level of reality beneath that of nano-technology.. The foundation of science is not some vague generality, but the exercise of reason as originating from the human sensorium. There is no difference between mathematical and ordinary inductive reasoning. |

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### Contents

PREFACE | 9 |

CHAPTER IITHE REJECTION IN BEHALF OF THE FINITE | 18 |

CHAPTER IIIIN DEFENSE OF THE IMMEASURABLE | 26 |

Copyright | |

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### Common terms and phrases

absolute numbers abstract actual infinity angle approximate argument axioms Ayn Rand base calculus century chapter circle Colin Maclaurin concept Consider continuity contradiction curve Dedekind defined definition derivative digits direction discrete distance division division by zero Einstein element endless equal Euclid fact finite number fraction fundamental geometrical Georg Cantor greater Henri Lebesgue Hilbert's axioms Ibid idea imaginary numbers immeasurable impossible induction infinite infinitesimal instant irrational magnitudes irrational numbers John Cook Wilson Kline Leibniz length Leonard Peikoff limit mathematician mathematics matter means measure minimum Morris Kline motion natural numbers negative numbers never number line number system objects parallel physical Pisaturo and Marcus positive number possible potential infinity quantity rational numbers real number real system reality reason rectangles rotation sense sequence set theory side spacial square root straight line subtraction Suppose symbol tangent unit velocity veritable number veritable system whole numbers zero