Uncomputable Probabilities
Are real numbers really real?
It turns out that if you choose a real number $x$ between zero and
one, $x \in (0, 1)$, and you have uniform probability of picking any real
number between zero and one, then the probability is unity that the
number $x$ will be uncomputable. The probability is zero that the number
will be computable.
Gregory Chaitin, How Real are Real Numbers
