Oleg Zabluda's blog
Saturday, September 10, 2016
 
"""
"""
a normal number is a real number whose infinite sequence of digits in every base b is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b^2 pairs of digits are equally likely with density b^−2, all b^3 triplets of digits equally likely with density b^−3, etc.
[...]
While a general proof can be given that almost all real numbers are normal (in the sense that the set of exceptions has Lebesgue measure zero), this proof is not constructive and only very few specific numbers have been shown to be normal. For example, Chaitin's constant [1] is normal. It is widely believed that the numbers √2, π, and e are normal, but a proof remains elusive.
"""
https://en.wikipedia.org/wiki/Normal_number

"""
Chaitin constant is a real number that informally represents the probability that a randomly constructed program will halt. [...] Although there are infinitely many halting probabilities, it is common to use the letter Ω to refer to them as if there were only one. [...] Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Indeed, each halting probability is Martin-Löf random, meaning there is not even any algorithm which can reliably guess its digits.
"""
https://en.wikipedia.org/wiki/Chaitin%27s_constant
https://en.wikipedia.org/wiki/Normal_number

Labels:


- posted by Oleg Zabluda @ 4:25 PM | permalink | | | technorati | bloglines | feedster
| |

Home

Powered by Blogger