Here’s a bird’s-eye view of what’s going on, why it trips up a lot of people, and how you could say it in two lines:
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- A more succinct statement
“You can’t pick a real number uniformly at random from all of ℝ, because if you tried to assign every point probability p, then p·∞ would have to equal 1, forcing p=0—and yet you still pick exactly one number. That “paradox” dissolves once you use probability densities (for intervals) instead of point-probabilities.”
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