Projective line at infinity
= Projective line at infinity
{title2=$\ell_\infty=\{[x:y:0]\}$}
After choosing the affine chart $z\ne0$ in the <projective plane>, its complement $z=0$ is the projective line at infinity. Affine parallel lines meet at the same <projective point> on this line, corresponding to their common direction. The choice of this line is part of the affine chart, not an intrinsic distinction preserved by every <projective transformation>.