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That argument works for any number. The probability of picking any particular number is zero, there's nothing special about rationals from that perspective. Thi
by kaashif 2y ago
That argument works for any number. The probability of picking any particular number is zero, there's nothing special about rationals from that perspective. This has no bearing on the measure of the set as a whole.
- jerf 2y agoWhich is why I very, very explicitly presented it as a way to gain some intuition and not as a rigorous mathematical argument. That wasn't an accident.
- kaashif 2y agoThe probability of picking a single number can't be used to determine the probability of picking a set. You can't build intuition this way. This is almost exactly the same thing as saying integrating x^3 from minus infinity to plus infinity is zero because each zero width line has zero area, so adding them all up is zero too. Gives the right answer by coincidence, but also works to show incorrect results.