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Actually it is not guaranteed that every string of bits will at some point be a substring of pi. Bad joke, since wrong.
by zyroth 19y ago
Actually it is not guaranteed that every string of bits will at some point be a substring of pi. Bad joke, since wrong.
- mojuba 19y agoCan you generate an infinite string of bits that does not contain a given finite string? Edit: no periods in the infinite string, of course
- rms 19y agohttp://en.wikipedia.org/wiki/Normal_number#Properties_and_examples http://en.wikipedia.org/wiki/Normal_number#Properties_and_ex... Sure... the infinite string of 1s, or the infinite string of 0s, or the infinite string of 0s and 1s that is made up of only decimal 3s and 7s. There are an uncountably many number of non-normal real numbers like this, even though the infinite amount of normal real numbers is bigger.
- mojuba 19y agoAlright, that makes sense, and how about pi?
- zyroth 19y agoSince pi is not random, we cannot say that every finite string is in it. (If it was, the probability P[s in binary representation] would be 1 for every finite s) Actually, there is no proof and no counter proof that every finite string comes up in pi. (...that I know of)
- zyroth 19y ago> There are an uncountably many number of non-normal real numbers like this, even though the infinite amount of normal real numbers is bigger. How sure are you with that one? Mind to supply a proof?
- rms 19y agoI have no proofs; I don't think very many proofs exist with regards to this topic. From what I've been able to gather, I think the cardinality of the normal and non-normal numbers are the same, even though the non-normal numbers are measurably greater because of probability distributions. This is a paradox that I don't really understand. http://forums.xkcd.com/viewtopic.php?f=3&t=4270 http://forums.xkcd.com/viewtopic.php?f=3&t=4270
- zyroth 19y agoAnything related to the concept of infinity tends to be hardly understandable in an "emotional" or "intuitive" way. We can just apply the rules of logic and accept.
- zyroth 19y agoYes, I can: 01001000100001... Guess what? There are uncountable ones.