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11 - Approximation of Irrationals by Rationals

Table of contents

  • 11.1 Statement of the Problem
  • 11.2 Generalities Concerning the Problem
  • 11.3 An Argument of Dirichlet
  • 11.4 Orders of Approximation
  • 11.5 Algebraic and Transcendental Numbers
  • 11.6 The Existence of Transcendental Numbers
  • 11.7 Liouville’s Theorem and the Construction of Transcendental Numbers
  • 11.8 The Measure of the Closest Approximations to an Arbitrary Irrational
  • 11.9 Another Theorem Concerning the Convergents to a Continued Fraction
  • 11.10 Continued Fractions with Bounded Quotients
  • 11.12 Simultaneous Approximation
  • 11.13 The Transcendence of e
  • 11.14 The Transcendence of \pi

11.1 Statement of the Problem

11.2 Generalities Concerning the Problem

11.3 An Argument of Dirichlet

11.4 Orders of Approximation

11.5 Algebraic and Transcendental Numbers

11.6 The Existence of Transcendental Numbers

11.7 Liouville’s Theorem and the Construction of Transcendental Numbers

11.8 The Measure of the Closest Approximations to an Arbitrary Irrational

11.9 Another Theorem Concerning the Convergents to a Continued Fraction

11.10 Continued Fractions with Bounded Quotients

11.12 Simultaneous Approximation

11.13 The Transcendence of e

11.14 The Transcendence of π


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