• John Gilbert
  • Camilla Jordan
Part of the Palgrave Mathematical Guides book series (MG)


In order to discuss continuity we need to consider ideas of limits. Consider the function f defined by
$$f(x) = \left\{ {\begin{array}{*{20}{c}} {2x + 1}&:&{x < 2} \\ {2x}&:&{x \geqslant 2} \end{array}} \right.$$
whose graph is shown in Figure 3.1. Let us see how we should show the function at x = 2. We cannot give it two values, since the value of f (2) is unique, and specified by the definition to be 4. In graphical terms, we could depict this by putting a small open circle at (2, 5) and a filled circle at (2, 4) as in Figure 3.1.




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Copyright information

© John Gilbert & Camilla Jordan 2002

Authors and Affiliations

  • John Gilbert
    • 1
  • Camilla Jordan
    • 2
  1. 1.Department of MathematicsUniversity of LancasterLancasterUK
  2. 2.Open UniversityUK

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