Extending the real numbers with 1 vs. 2 points at infinity both have applications where they model real situations. For example, if we take a mercator projecti

Extending the real numbers with 1 vs. 2 points at infinity both have applications where they model real situations. For example, if we take a mercator projection of the globe onto a 2-infinite-ended cylinder, the latitude coordinate could meaningfully be either +∞ or –∞. If we take the stereographic projection of the globe onto the plane, every pair of coordinates with one infinite value corresponds to the same point on the sphere.