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Sep 7, 2015 at 19:25 comment added Garabed Gulbenkian This is a very nice approach which looks as if it would work, although I do not know if I would be able to fill out all the details of a rigorous proof. It would seem, then, that we could define an ascending chain of subsets of the set of computable functions-starting with the set of primitive recursive functions- and classify a computable real number r by the smallest set in the chain containing a function that determines a Cauchy sequence of rational numbers which converges to r.
Sep 7, 2015 at 18:55 vote accept Garabed Gulbenkian
Sep 6, 2015 at 18:06 history answered Bjørn Kjos-Hanssen CC BY-SA 3.0