Consider a hypothetical dart and target. The target is defined as a circle that encloses an infinite number of points. The dart is a line segment that pierces the circle at right angles at point P.
You pick point P to aim at and throw the dart at the target. What are your odds of hitting point P?
Point P exists as the intersection of a plane with no thickness and a line of no width. P is a single point out of an infinite number of points so the odds are:
1/∞ = 0
Surprisingly, you have no chance of ever hitting point P. This appears to be contradicted by the fact that the dart does, indeed, hit the target. This is what I call Aqualung's Paradox for historical reasons.
If we can add one to something, it makes it bigger. If we subtract one from something, it makes it smaller. A more flexible calculation of the odds might be:
1/(∞ - 1) > 0
Thus, we end up with a result that is technically equal to zero, but not exactly equal to zero. Since the odds are not exactly zero, you might hit P on the very first try.
But I wouldn't bet on it.😉
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