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Rational numbers are impossible!

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Dan Stoppelman wrote:

I can't pretend I understand all of this, but the 0% thing doesn't make sense to me. Just because the dart has a 0% chance of hitting a specific real number you choose in advance doesn't mean it won't hit a different real number on its own. Even if it's impossible to identify which number it did hit, that doesn't mean it will never hit a real number. In fact given infinite throws, doesn't the chance of hitting a real number at least once become 100%? If so, how can it ever have been 0%?

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