6 ms·
> Your chances: > 3 or fewer letters: about 100% > 7 or more letters: about 0%. While this might be true for the set he's calculated, doesn't an infin
by alttag 15y ago
> Your chances:
> 3 or fewer letters: about 100%
> 7 or more letters: about 0%.
While this might be true for the set he's calculated, doesn't an infinite sequence of non-repeating digits suggest the likelihood of every sequence approaches one as the number of digits are calculated approaches infinity?
- bostonpete 15y agoYes.
- yequalsx 15y agoNo! Consider this number: 0.101001000100001..... (continue the obvious pattern) This number is irrational but there is an obvious pattern to the digits. The pattern is not random. It's an open question on whether or not the digits of pi are randomly distributed. If so then what you write is correct.
- cabacon 15y agoDoesn't the difference between just being irrational (e.g., sqrt(2)) and being transcendental (e.g., \pi, e) matter here?
- yequalsx 15y agoThe claim I responded to had to do with the randomness of the digits of a number. The person appeared to have the belief that irrational numbers have to have random digits. This isn't true. This isn't true for transcendental numbers either. The number I gave is transcendental but doesn't have random digits.
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- dmg8 15y agoI immediately thought that same thing. Someone else posted this link (http://math.stackexchange.com/questions/20566/prove-there-are-no-hidden-messages-in-pi http://math.stackexchange.com/questions/20566/prove-there-ar...) which answers the question: if Pi is a "normal number" -- a number whose expansion in base b asymptotically contains each digit 0, 1, ..., b-1 with equal frequency, for any give b -- then within that numbers expansion (in any base) you'll find every finite string composed of those digits infinitely many times. So normal numbers will not only contain any person's name, but every book ever written, every law of nature, etc. Wikipedia says that Pi is widely believed to be normal, but that it's not been proved. It's interesting that almost every real number has this normality property (in the sense that the set of real numbers that are not normal has Lebesgue measure zero), as it sounds like a very restrictive criteria.