Hi, On 3/15/07, Andreas Harnack <ah.boost.04@justmail.de> wrote:
Hi Ben, interesting stuff, it just leaves one question to me: How can you represent an affine point in a computer program? My guess is: you can't.
You can, as you describe yourself in the following sentence:
But you can implement vector spaces and you can map an affine space to a vector space by choosing a basis, i.e. an origin and a set of orthogonal unit vectors.
...except that this is a (Cartesian) _coordinate system_, not a basis. A basis is a minimal set spanning a vector space.
I'm not sure if the following is correct, but may be we can define affinity as the whole of all possible representations
Just as you could define a vector space as the whole of all its bases (although one is certainly sufficient ;-).
Affine spaces and vector spaces are two different things that live without each other, [...]
Not quite; you need a vector space to define an affine space, for the difference between two points lives in that vector space. Regards, Michael