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Parallel Lines:
1) I've been told that parallel lines never meet - except at infinity.
2) Also that a straight line is a circle of infinite radius.
3) Surely if you get two infinitely large circles such that they don't overlap, at their closest point they are straight (as per 2) and parallel yet must both meet (by 1) and not as per 3) - not overlapping.
Any suggestions? (I'm confused!)

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