Donald wrote,
"Could you give us you mathematical definition for the randomness of that particular set of numbers?"

Hi Donald,

Yes. From my post just above, it is "... the ratio of the information dimension (D_i) of the set to the capacity dimension (D_c) of the space it occupies."

The calculation not only takes into account the distribution of the numbers, but also the sequence. Thus, the same set of integers, in 1-dimensional integer space of {1 - 10}, could be random in another order, but not in the order written.

I don't know how to make it any more intuitive than with the coin toss example in my previous post. If you can look at a result set and declare that the set is not random with absolutely no knowledge of the process by which the set was generated, then you have demonstrated that randomness is inherantly independent of process.