What is the probability that a randomly chosen number from the set of c.e.numbers is period(number)?


What is the probability that a randomly chosen number from the set of computable numbers is period(number)?


For definition of period(number),please see www.maths.ed.ac.uk/~aar/papers/kontzagi.pdf‎.


Further more,if we replace period number with exponential periods,what are the probability in the question above?


The set of computable numbers includes set of periods or exponential periods ,what is the reverse?Is it true?or almost true in probability sense?



What is the probability that a randomly chosen number from set of c.e.number is period(number)?
[This paper](http://arxiv.org/pdf/0805.0349.pdf) by Yoshinaga shows that periods are contained within a proper subclass of the computable reals. Another proof is given in [this paper](http://wwwmath.uni-muenster.de/mjm/vol_3/mjm_vol_3_04.pdf) by Tent and Ziegler. (Disclaimer: I haven't read either paper myself.) Whether the results in these papers answer your questions or not depends, as Joel points out, on what you mean by "randomly chosen".


