• Sterling K. Berberian
Part of the Undergraduate Texts in Mathematics book series (UTM)


In elementary calculus, continuity and derivatives are painted with the same brush and the brush is called ‘limits’; this is good for showing the core of unity in the processes of calculus. However, when we look at these concepts more closely, they are quite different: continuity has to do with the interaction between functions and open sets, whereas differentiability involves in addition the algebraic structure of the number field (from the very outset one considers ‘difference quotients’).


Continuous Function Rational Number Constant Function Inverse Image Neighb Orhood 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Sterling K. Berberian
    • 1
  1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA

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