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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