Take the tour ×  If we enumerate* all the computable numbers,
those for which there exist a turing machine that outputs its
digits to arbitrary precision. What is known about the
asymptotic density of rationals, irrationals, algebraic, normal
and transcendental numbers in this set?  *Enumerate them by
their Kolmogorov complexity, ie we enumerate all turing programs
up to a total character length n, then take the limit as n
approaches infinity, does any of the number types have a
limiting density in this set?  share|improve this question
Please define relative density. –  Rasmus Oct 27 '11 at 15:30
Doesn't that depend drastically on the enumeration you choose?
You can just play Hilbert's hotel and take another enumeration:
first 10 irrationals, then 27 transcendentals, then 1 rational
and repeat this pattern, so I'd be surprised if this question is
well-posed. –  t.b. Oct 27 '11 at 15:41 Here's a somewhat
related thread –  t.b. Oct 27 '11 at 15:50 @Raphael: No. For
each positive integer $n$ the multiples of $n