RE: The nature of number
July 30, 2012 at 2:39 am
(This post was last modified: July 30, 2012 at 2:39 am by CliveStaples.)
(July 29, 2012 at 9:17 pm)Categories+Sheaves Wrote: 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)
But if many points on the line are mapped to the same point, then the mapping isn't invertible...
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