Two parallel lines can intersect.

Ave. Con asked me why I think he's trying to define his way to victory. This is an odd request from my viewpoint, because I articulated my reasoning in an entire paragraph. Firstly, I don't think Con, when typing out his argument, was actually thinking of using definitions to win the debate. I just think that his definitions can't be accepted because they're not neutral. Remember my analogy to a debate about public v. s. private health care, and one side tries to define public health care as 'a health care system that is inferior to private health care'. It defines public health care in a way that assumes the very thing we're debating. On the same token, defining parallel lines as 'not meeting' is just assuming what we're supposed to be debating. The definitions should be rejected for that reason. I understand that it's important to have clear definitions for a debate's resolution. However, all of the terms in the resolution were defined in the first round. There was no need for Con to post any new definitions because all of the relevant definitions had been given. Now, let's return to geometry. I think it's peculiar to claim that parallel lines can't intersect. It has very strange implications. Is projective geometry, where 'parallel lines may intersect', completely wrong? [1] Of course it isn't. They intersect just fine. How, then, can one argue that parallel lines cannot intersect? Con states that an axiom of the geometries I'm using is that parallel lines intersect at an infinity. This might be true for some non-Euclidean geometries, but the geometry I used, hyperbolic, has no such axioms. Con doesn't provide any sources in this entire round, so there's no reason to believe that this is true other than his word. His word is wrong, and I even consulted my math teacher to see if this claim was true. She said it wasn't. There is no reason to believe that this an axiom of the geometries I'm using. Con proceeds to give an argument that is, in my opinion, bizarre. Remember, I gave an argument in favor of the resolution based on hyperbolic geometry. This is the geometry of what is called a "saddle", which can be seen in the last picture. Hyperbolic geometry does not deal with flat surfaces, but surfaces with curvature. Con's argument, which talks about you and your friend driving cars, deals with flat surfaces. There is no way to demonstrate my argument to be false using flat surfaces, because you're dealing with different geometries. [2] Besides, the entire argument is predicated on an unsupported claim, which is that my geometries have the axiom of 'two parallel lines intersect at infinity'. This debate isn't about one specific geometry. It is about any form of geometry. [3] I only need to show that parallel lines intersect in one, such as hyperbolic or spherical. It could be the case that parallel lines do not intersect when you're dealing with flat surfaces. This does not mean Con has won the debate, because all I need to do is show that they intersect when dealing with something else, like saddles. The argument from saddles hasn't been answered to, because there is no way to move from 'parallel lines do not intersect when dealing with flat surfaces' to 'parallel lines do not intersect when dealing with saddles'. It is a non-sequitur. In conclusion, there are no reasons to think that parallel lines cannot intersect. I have given a good example of a case where parallel lines do intersect. I have also provided more sources than Con has, so my factual assertions have more weight than Con's. Therefore, the preponderance of evidence favors a Pro vote. Vale. References1: . http://robotics.stanford.edu...2: . http://en.wikipedia.org...3;