Random Numbers in 0, 1

Generate a sequence of numbers between 0 and 1 picked at random.

By saying at random, we wish for two subintervals of (0, 1) of the same length to have the same probability of containing a generated number.

For a random number $z$: $Pr(z\in (0,\frac{1}{2}))=Pr(z\in (\frac{1}{2},1))$