The nature of number

[Categories+Sheaves]

Can you explain "0x +n" functions again? I'm not clear on what the domain and codomain are, let alone how the points are mapped.

It's essentially this way of creating a mapping between lines A and B in the plane via some point c (preferably not lying on either line, but it counts as "x0" if c lies on B)--point a on line A is mapped to the intersection of the line ac with B

I'm looking at projective transformations*, (these can be represented as 2x2 matrices) and saying jonb's functions are precisely the ones whose bottom row is [0 1]** (for "xa +n", the top row is [a n]). Technically then, they're just affine transformations, but I'm trying to work through Beltrametti et. al's book on projective varieties and I like the projective lingo

*this acts on some projective coordinates set on the lines in question.

**it's [0 1] as long as the two lines are parallel. If you want to do this for two lines in the euclidean plane that aren't parallel, this will change to [0 m] for some m. You only see action in the bottom-left entry when the projectivity maps some coordinate to the 'point at infinity' (which jonb is not talking about)