The point at infinity can also be added to the complex plane, , thereby turning it into a closed surface known as the complex projective line, , a.k.a. Riemann sphere. (A sphere with a hole punched into it and its resulting edge being pulled out towards infinity is a plane. The reverse process turns the complex plane into : the hole is un-punched by adding a point to it which is identically equivalent to each and every one of the points on the rim of the hole.)
Now consider a pair of parallel lines in a projective plane . Since the lines are parallel, they intersect at a point at infinity which lies on 's line at infinity. Moreover, each of the two lines is, in , a projective line: each one has its own point at infinity. When a pair of projective lines are parallel they intersect at their common point at infinity.
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