I meant to say all _real_ solutions of polynomials, etc. At 12:34 PM 2/15/2010, Henry Baker wrote:
This may be what you want: "real closed fields" encompass all of the solutions of polynomials with integer coefficients & is closed under addition, subtraction, multiplication & division & roots & powers (so long as the roots & powers have fixed constant integer roots & powers). [I believe that the second half of the previous sentence is redundant.]
Clearly the elements of real closed fields are a countable set.
At 11:41 AM 2/15/2010, Dan Asimov wrote:
. . . real numbers that can be expressed using integers, addition, subtraction, multiplication, division, and integer roots and powers -- starting with integers or rationals?
How about all such (real or) complex numbers?
(As distinguished from the rest of the algebraic numbers.)
--Dan