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Maybe not the most formal of meanings, but my favorite is a probabilistic one: given a random element, how likely it is that it satisfies a predicate? If some e
by js6i 5y ago
Maybe not the most formal of meanings, but my favorite is a probabilistic one: given a random element, how likely it is that it satisfies a predicate? If some elements don't, but it's still satisfied with probability 1, that's pretty clearly almost always.
EDIT: yeah you guys are right, I wouldn't worry too much about the prior not being a proper distribution, but still - this doesn't seem related to the cardinality of sets in a simple way after all!
- btilly 5y agoRandom according to what distribution? The probability distribution that we all want to define on the real numbers does not exist. And this has non-trivial consequences.
- deleted 5y ago[deleted]
- Nevermark 5y agoI think for infinitely sized sets this isn't so simple. For instance, what is the random distribution you are using to select from a set of infinite numbers? The cardinality of any two intervals of real numbers is the same, regardless of the lengths of the intervals.