Two days ago I thought the new version was complete but when I was reading it again I realized there are ambiguities and new things should be defined and constructed. I think only one new thing should be added so that the new version is complete, but, again, new errors might be found as I’m proceeding. Also since the structure has been modified a lot maybe there is a simpler, more concise way to organize it. Currently based on R, a vector space is built and then the vector space is used to construct an extended version of R. It might be unclear for readers but I couldn’t think of any other way to construct the extended R.
A new zero zone should be added. I’ll finish this version and then rewrite it because some of the functions should be constructed again. It’ll be submitted when the revision is done.