## Irrational Numbers |

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### Contents

Rationals and Irrationals | 1 |

Simple Irrationalities | 15 |

Certain Algebraic Numbers | 28 |

Copyright | |

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absolute values algebraic integer Amer arbitrarily small assume bers complex numbers conjugates contradiction convergents Corollary countable cyclotomic polynomial decimal expansion defined degree divisor establish factor field R(8 Fn(x follows functions given Hence hi/ki hn/kn implies infinite simple continued irrational number irrationality irreducible irreducible polynomial Jp[x lattice point linear linearly Math mathematical mathematical induction measure zero minimal polynomial monic monograph multiple N(Bk natural numbers normal number normal to base notation Notes on Chapter nth root p(nr permutation polynomial f(x positive integer positive rational prime primitive nth root proof of Theorem prove quadratic irrational rational coefficients rational integers rational integral coefficients rational numbers real numbers replaced result root of unity satisfies the inequality sequence simple continued fraction simply normal sufficiently large symmetric polynomial Theorem 2.5 Theory tion transcendental numbers unique unit interval write