37 ms·
hmm probably
by ark4579 3y ago
hmm probably
- contravariant 3y agoProbability theory works, with 100% chance even. Which annoyingly isn't the same as always.
- bmacho 3y agoWhat is funny thought, that 0% chance events don't can't happen, but must happen. Like when you pick a point on a line, or roll a dice infinitely many times.
- quantum_state 3y agoThe concept of probability is based on the concept of measure in math => limitation in its description of things, e.g., the probability for a real number in [0, 1) being an irrational number is 1.
- eli_gottlieb 3y agoHold on, what measure over the unit interval assigns probability 1 to the set of irrational numbers in the unit interval? Do irrational numbers on their own even form a proper measurable set?
- omnicognate 3y agoLebesgue measure [0]. I never did write part 2 and many years have gone by with that blog languishing unmaintained on free wordpress but I wrote a thing that goes through the issues around this [1]. [0] https://en.m.wikipedia.org/wiki/Lebesgue_measure https://en.m.wikipedia.org/wiki/Lebesgue_measure [1] https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-and-filtrations-in-probability-theory-part-1 https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-...
- contravariant 3y agoThe irrationals are measurable for any measure that can measure points, which is most of them.
- hgsgm 3y agoOf course. [0,1] has measure 1. Rationals have measure 0. Irrationals have measure 1-0=1 This question is why measure theory exists.
- throwme_123 3y agoHMMs are probabilistic models, yes.