Wednesday 12 February 2014

Monotone real valued function which is discontinuous only at rationals.

There are examples of real valued functions which are continuous at irrationals and discontinuous at rationals. But i am trying to find such a monotone function. I don't know how to think this types of examples. I wants such types of simple examples not too much complicated so that each and everyone can easily digest it. I tried many simple examples but did't got. In the book Counterexamples in Analysis by Bernard R. Gelbaum and John Meigs Hubbell Olmsted there is given a way to construct such types to examples, but i like simplest such types of example. Please try to give such type of example. Thanks in advance.

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