Talk:Hyperplane at infinity

Generality

The article, before my edits of today, was written in terms of real affine and projective spaces only. Actually, it applies to all affine and projective spaces, coordinatized by any field or division ring, or without coordinates. Possibly more examples (real, complex, finite?) would be desirable, but I suggest these belong in projective geometry. Zaslav 09:30, 13 November 2006 (UTC)[reply]

Possible Error

I am a beginner at this subject so will not attempt a correction. However I wonder if there is an error. In page Projective_space, I see an example of the projective plane P²(R) in which the points [x : y : 0] are said to be the line at infinity. That is, it appears that you zero one coordinate of the homogeneous coordinate form to get the something at infinity. This causes me to wonder whether the current page should read

"the equation $x_{n+1}=0$ defines a hyperplane at infinity"

rather than, as it currently does,

"the equation $x_{n+1}=1$ defines a hyperplane at infinity".

Could someone more knowledgeable please either make a correction, or else explain to me why one is not necessary? - Thanks — Preceding unsigned comment added by 83.217.170.175 (talk) 06:22, 1 November 2013 (UTC)[reply]

Zero or one is okay. In fact, when one coordinate is set to a constant, then a hyperplane of the projective space is determined. As stated, any hyperplane may be taken as the one at infinity, given that they are all equivalent under the projective group.Rgdboer (talk) 21:02, 1 November 2013 (UTC)[reply]