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And, I don't know JP. It's been on my mind for some time now, if I assume that parallel lines can merge then the idea of them 'crossing' is just a small step to take. But the axiom is that they can't intersect, and it makes sense to me. If I assume a equal distance between those parallel lines then it seems to me that this distance should stay assuming that the lines are parallel. At least as long as it is in a 'plane', like drawing it on a paper.

No JP, I used the triangle on a sphere as a definition that I found understandable but my question here is how two parallel lines can be seen to cross, and as I've seen it described 'merge'? As I see it there must be a space between those lines, and at no point will they share a same point (a slight pun, still, how I see it). And it's a axiom to me, as self evident as picking up those stones to me to count.