Quote by Loren Booda
What is the average number of intersections for two infinite curves confined to a plane?

How long is a piece of string?
Seriously, one can think of an infinite number of curves that intersect an infinite number of times (such as say y=sin(x) and y = 0). Equally, one can think of an infinite number of curves that intersect once (y = x and y =x) or not at all (y=0 and y=1).
Perhaps I am missing the point of the question, but to me it doesn't make sense.