Mathematically speaking, randomness is simply when the value taken by a
variable at time (or position)
i is completely independent of the values of the variable at all times not
i. In other words, the
correlation between
xi and
xi+h is equal to zero for all values of
h.
It is a useful mathematical concept, but one difficult to put into practise; for example, all algorithmic random number generators in fact produce pseudo-random numbers, which means that the periodicity in the numbers generated exists, but has a very long period.