= Point at infinity of the complex projective line
{title2=$\infty=[1:0]\in\mathbb{CP}^1$}
In the affine coordinate $z\mapsto[z:1]$, the complex <projective line> consists of the <complex plane> together with the single extra <projective point> $[1:0]$, called its point at infinity. It is the only point whose second <homogeneous coordinate> vanishes. This coordinate choice distinguishes the point; it is not intrinsically special under <projective transformations>. The map $[u:v]\mapsto[v:u]$ exchanges zero and infinity. The resulting one-point compactification is the <Riemann sphere>.
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