In the same plane, two lines that don't want to intersect are parallel lines. There must be the word "straight line". The axiom of parallel lines is an important concept in geometry. The axiom of parallelism in Euclidean geometry can be equivalently expressed as "only one straight line is parallel to the known straight line at a point outside the straight line".

Axiom of parallel lines

Its negative form "there is no straight line parallel to the known straight line at a point outside the straight line" or "there are at least two straight lines parallel to the known straight line at a point outside the straight line" can be used as a substitute for Euclidean geometry parallelism axiom, and a non-Euclidean geometry independent of Euclidean geometry can be derived. In advanced mathematics, the definition of parallel lines is that two lines intersecting at infinity are parallel lines, because there is no absolute parallelism in theory.