Projective geometry of the real line

Projective geometry of the real line involves studying properties of points and lines that remain unchanged when addition or projection transformations are applied. It extends the usual number line by adding a point at infinity, allowing for a unified approach to intersections and directions. This framework treats lines as loops where parallel lines meet at infinity, simplifying concepts like perspective and perspective transformations. Essentially, it provides a way to analyze geometric relationships that are invariant under projection, revealing deeper symmetries and connections even when the line is extended beyond its finite bounds.