>> Having said that, we can define a special group of coordinate >> systems for the Euclidean plane---the Cartesian coordinate systems, > >Right. They are the ANALOGY of the inertial frames in relativity. > > But they don't form a group, they form a set or a class. > "Group" is a technical word with a different meaning than > you intended. The transforms between pairs of such coordinates > form a group.
I was not meaning "group" in the technical sense, I was just meaning it in the sense of a collection. But actually, don't they form a group? The various Cartesian coordinate systems are related by operations such as (1) translations, (2) rotations, (3) scale transformations. Couldn't they form a group?