Oops, instead of "roots", I meant "n-th roots". Hmmm. So "constructible" won't work for what I wanted. Nevertheless, "constructible" = "ruler&compass constructible" = "rational+sqrt" is still useful. Thanks. At 08:12 AM 10/17/2012, Michael Kleber wrote:

I would expect "constructible" to be short for "ruler-and-compass constructible", so to only allow square roots.

--Michael

On Tue, Oct 16, 2012 at 9:30 PM, Henry Baker <hbaker1@pipeline.com> 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:

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On Mon, Oct 15, 2012 at 10:45 PM, Henry Baker <hbaker1@pipeline.com> wrote:

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"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