All examples of a dense and co-dense set I have seen are either of full...
All examples of a dense and co-dense set I have seen are either of full Lebesgue measure or of measure zero. For instance, in restriction to the unit interval , we could have respectively or . What I am looking for is a dense and co-dense subset such that
I have attempted this task sequentially by, ever more finely, nibbling holes out of subintervals of and partially back-filling the previously created holes. It's easy to approach half measure at each step, but I can't see how to to get convergence.