# Real analysis

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}.

https://brainmass.com/math/real-analysis/constructing-functions-discontinuities-28573

#### Solution Preview

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. ...

#### Solution Summary

The solution shows how to construct functions with discontinuities.

$2.49