Most of my equations involve intersections. One equation, for example, may be a plane and the other another plane. The solution is the place where the the two planes meet. It is a line. One variable is removed in the solution.
I had one equation #24 that had a squared variable. I substituted another equation in for one of the squared terms. The other squared term remained. It worked, however, what does this mean? I searched and could not find an authoritative explanation. After 5 years, just yesterday it hit me. It's a union. I have done intersections A&B and unions A or B with logic but never with equations. The union introduced a additional degree of freedom and another variable. The union includes the domains of both equations. Now I know this and edited my book to incorporate this understanding. I know, who cares, however, discovery is fun. Frank Znidarsic
