Unfortunately, "constructible number" is a term already used for, essentially, a number that is constructible in the plane using the classical constraints of straightedge and compass. So, e.g., 2^(⅓) is not constructible. I apologize for parsing your last question incorrectly. But I'd definitely agree with Michael where he says the usual terminology for what you are defining is [not] expressible in radicals. --Dan On 2012-10-16, at 6:30 PM, Henry Baker wrote:
Perhaps we can call an algebraic number that can be represented with rational ops and roots a "constructible" number.
Then what I want is a non-constructible algebraic number.
Is there a shorter and/or traditional name for non-constructible algebraic number?
At 05:56 PM 10/16/2012, Michael Kleber wrote:
On Mon, Oct 15, 2012 at 10:45 PM, Henry Baker <hbaker1@pipeline.com> wrote:
"Transcendental" means not the root of any finite polynomial with integer coefficients.
http://en.wikipedia.org/wiki/Transcendental_number
Is there a name for a number which isn't algebraic for a _solvable_ Galois polynomial -- i.e., a number which can't be constructed by rational & root operations?
I think the most common description would be "[not] solvable/expressible by radicals". I don't know of a dedicated term for either state.
--Michael
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