In a lecture the professor drew two lines, a and b, parallel to each other. The professor then asked if line a is parallel to itself.
The students said no because the definition of a parallel line is that it never cuts another line and a cuts itself all the way through.
The professor said that this is wrong, of course a is parallel to itself.
Is the professor asuming that the lines are transparent and thus do not cut each other? Are the students using the wrong definition of parallelism? Who is right, and why?