Whilst working with the equations for the previous post on the fusc function, I encountered one I wished to invert. That equation was essentially
but I had not noticed that this equation is special, and that the ‘2’ is significant.
I recently encountered a collection of related articles regarding an amazing explicit enumeration of the non-negative rational numbers. Whilst experimenting with the mathematical constructs described, I made some discoveries of my own (which I doubt are new, but I have not found them described elsewhere).
Below, are the references and links to those articles. They’re all worth a read.