A Prequel to Transcendence: The nature of numbers and the irrationality of \( \sqrt 2 \)
  • Edward B. Burger
  • Robert Tubbs


The study of the nature of numbers is one of the most ancient and fundamental pursuits in all of mathematics. Before we embark upon our journey into the world of transcendental number theory, we offer this brisk panoramic tour of the notion of number in which we not only introduce some basic background, but, more importantly, attempt to provide a framework within which the theory of transcendence will find its rightful place in our quest for an understanding of the intrinsic properties of numbers.


Natural Number Complex Number Rational Number Cauchy Sequence Algebraic Number 
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Copyright information

© E.B. Burger and R. Tubbs 2004

Authors and Affiliations

  • Edward B. Burger
    • 1
  • Robert Tubbs
    • 2
  1. 1.Department of MathematicsWilliams CollegeWilliamstownUSA
  2. 2.Department of MathematicsUniversity of Colorado at BoulderBoulderUSA

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