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Real analysis

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For each of the following choices of A,construct a function f:R->R that has discontinuities at every point x in A and is continuous on A^c(compliment)
a-A=Z
b-A={x:0<x<1}
c-A={x:0<=x<=1}
d-A={1/n:n belong to N}.

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Solution Summary

The solution shows how to construct functions with discontinuities.

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I construct the function f: R->R which is discontinuous at every point in A and is continous at each point not in A.
a. ...

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