Numbers in General

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The rational numbers are beautifully suited to arithmetic, being closed under +, −, x, ÷, but they are inadequate for geometry. Their inadequacy is exposed by the Pythagorean theorem, according to which the diagonal x of the unit square (Figure 3.1.1) satisfies x2 = 12 + 12 = 2. We can see that no rational number x satisfies this equation as follows.

Keywords

Fundamental Theorem Algebraic Number Irrational Number Pythagorean Theorem Rational Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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