Hatto von Aquitanien a écrit : > Denis Feldmann wrote: > >> Hatto von Aquitanien a écrit : > >> Of course you are trolling, > > Uh, no. I'm very much attempting to engage in honest dialog.
> >> but it will be hard, even for you, to >> explain that the slight detail of forgetting to define the operations of >> your vector space doesn't matter at all here. > > Hu? Do you know how to work with vectors in a Euclidian a plane?
It happens I do. But your thing is not yet an Euclidian space. What isq the formuma or the metric?
If so, > that's all you need to know. If you want the math to produce the mapping, > it's trivial.
If you say so...
> >> While we are on it, I >> wonder why you insist on suppressing the north pole : a slight (or tot >> so slight) complication of the map would take care of that. > > Unless I use the notion which I presented in my earlier post, of splitting > the neighborhood of the north pole and wrapping it around infinity, I don't > see how I can produce a complete bijective map.
> >> And of >> course, there is no way you would get a subspace of R^3, but then again >> this is not to bother you, is it? > > Well, I'm not convinced of that.
At this stage, it is clear you are trolling. No one could be *that* dumb...
I have not insisted that I can do such a > thing in a way that would be acceptable to others. Nonetheless, if the > mapping is isomorphic to Euclidian R^2, then I have an equivalence relation > between the coordinate system on the sphere and the Euclidian plane. It > appears to be a matter of whether people accept that as justification for > calling the mapping on the sphere a subspace R^3. At this point, I really > don't care.