Final answer:
Incidence geometry allows for models where the parallel postulate does not hold, resulting in situations where lines l, m, and n can be parallel in pairs (l // m, m // n) but not all three together (l // n).
Step-by-step explanation:
In incidence geometry, there are models where the parallel postulate of Euclidean geometry does not hold. This means that even if we have lines l, m, and n where l is parallel to m (l // m) and m is parallel to n (m // n), it does not necessarily imply that l is parallel to n (l // n). One such model is the affine plane of order n, where parallel lines are defined as not intersecting, but there can be more than one line parallel to any given line through a given point. For example, consider a geometry on the surface of a sphere (spherical geometry), lines defined as great circles. Here, there are no parallel lines, since all great circles intersect, yet we could draw a diagram showing l, m, and n as seemingly parallel by Euclidean standards, but eventually meeting at points not shown on a simple 2-dimensional projection.