I think they do deserve to have their own name if they don't already. ((( (Could the word "surd" have precisely this meaning, or does that word either have only a vague definition, or a more limited precise definition?) Otherwise, some word with a sense similar to "constructible" would be a good candidate. And < thesaurus.com > has no listing for "constructible". ))) I think Marc's suggestion of "solvable" numbers is an excellent one. I don't think this term is taken, and "solvable numbers" is nicely consistent with Bill's comment that these numbers are precisely those having a solvable Galois group. If no one objects, then by the powers invested in me by the Math Goddess I hereby declare "solvable" the official name of such numbers. --Dan Bill Thurston wrote: << These are, in other words, algebraic numbers with solvable Galois group, which may be a reasonable way to specify them. Do they deserve to have a 1-word name? It would be tempting to call them "radical numbers" except that they're not actually so radical, they're comparatively tame among algebraic numbers. "Constructible numbers" is already taken, by the special case of algebraic numbers whose Galois group is a 2-group. Bill On Feb 15, 2010, at 2:41 PM, 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.)
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