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If you select a random point from [0, 1] segment, then probability of selecting that particular point is zero. Not "very close to zero", but "exactly zero".
by deepsun 8y ago
If you select a random point from [0, 1] segment, then probability of selecting that particular point is zero. Not "very close to zero", but "exactly zero".
- a_e_k 8y agoYep. That's why one speaks of probability density functions and not just probability functions.
- levythe 8y agoIt is not equal to zero. It is infinitesimal. There is a difference.
- Sharlin 8y agoInfinitesimals don't exist in standard analysis. There exist no positive numbers smaller than all positive real numbers. The probability of picking any given real number from [0, 1) is exactly zero, there's no other number it could be. Rigorously, the measure of any countable subset of real numbers is zero.
- deepsun 8y agoHonestly, I don't really "like" real numbers, exactly because they are defined as classes of equivalence of converging sequences of neighborhoods. But I'm pretty sure even in rational numbers probability would be exactly zero, because that's how probability there is defined (as a limit of a sequence, and limit is zero).
- brlewis 8y agoI want your random number generator.
- Beldin 8y agoActually, to be pedantic, the probability is one. Not "very close to one", but "exactly one". P (X | X) = 1.
- Dylan16807 8y agoGood thing telescopes aren't 0 in size.