Modifications of Thomae's Function and Differentiability

@article{Beanland2009ModificationsOT,
  title={Modifications of Thomae's Function and Differentiability},
  author={Kevin Beanland and James W. Roberts and Craig Stevenson},
  journal={The American Mathematical Monthly},
  year={2009},
  volume={116},
  pages={531-535}
}
  • Kevin Beanland, James W. Roberts, Craig Stevenson
  • Published in
    The American Mathematical…
    2009
  • Mathematics, Computer Science
  • As we shall see later, Thomae's function is not differentiable on the irrationals. In this note, we address whether there is a modification of Thomae's function which is differentiable on a subset of the irrationals. In Section 2, we prove that Thomae's function is not differentiable on the irrationals and define modified versions of Thomae's function. In Section 3, we show that for each of our modifications there is a dense subset of irrationals on which, quite surprisingly, the function is… CONTINUE READING

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