Functions: pathological, peculiar and extraordinary

  • A. R. Rajwade
  • A. K. Bhandari
Part of the Text and Readings in Mathematics book series (TRM)

Abstract

One of the first standard examples of a real-valued function that is discontinuous everywhere is
$$f(x) = \left\{ {\begin{array}{*{20}{c}} {1,} & {{\text{if }}x \in \mathbb{Q}} \\ { - 1,} & {{\text{if }}x \notin \mathbb{Q}} \\ \end{array} } \right.$$

Keywords

Rational Number Closed Interval Open Interval Irrational Number Binary Expansion 
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

© Hindustan Book Agency 2007

Authors and Affiliations

  • A. R. Rajwade
    • 1
  • A. K. Bhandari
    • 1
  1. 1.Panjab UniversityChandigarhIndia

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