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Do you know of any proof for that? My math intuition is telling me that randomly picking a real number is guarenteed to be irrational, based on the fact that th
by gizmo686 14y ago
Do you know of any proof for that? My math intuition is telling me that randomly picking a real number is guarenteed to be irrational, based on the fact that there is an uncountable infinity real numbers, but only a countable infinity of rational numbers. But, without assuming a probability of 0 means impossible, I do not know how to go about proving/disproving this.
- hypersoar 14y agoWe can't really pick "random real numbers" in any practical sense, so this is pretty much a theoretical distinction. It's essentially a matter of definition. The rational numbers have probability zero of being drawn, but they still lie in the sample space. One way to see it is this: The probability of picking any particular point in the interval is 0. But that doesn't mean that picking that point is impossible. _Some_ point has to show up when you pick one at random.