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re: What is a Random Number?

damien morton — Thu, 07 Oct 2004 00:50:00 GMT

A good paper of random numbers can be found here:

"Random Generators and Normal Numbers"
David H. Bailey and Richard E. Crandall
http://crd.lbl.gov/~dhbailey/dhbpapers/bcnormal-em.pdf

"We call a real number b-normal if, qualitatively speaking, its base-b digits are “truly random.” For example, in the decimal expansion of a number that is 10-normal, the digit 7 must appear 1/10 of the time, the string 783 must appear 1/1000 of the time, and so on.

It is remarkable that in spite of the elegance of the classical notion of normality, and the sobering fact that almost all real numbers
are absolutely normal (meaning b-normal for every b = 2, 3, . . . )"