A definition of 'random' requires of an unbiased random sequence that all of its subsequences of a given length appear with the same frequency. This is impossible if the sequence is finite with an 'alphabet' of 2 or more characters. For example, using a binary alphabet, if the sequence is n characters long, then there will be only 1 or 2 subsequences n-1 characters long. So if n is 6 then there will not be enough subsequences with 5 characters. There will be only 1 or 2 in the sequence, but there are many more possible 5 character long binary subsequences that therefore cannot be part of the sequence.
So we must fall back on the concept of 'disorder' for finite sequences.
(to be continued later)
