Invisible wrote:
>>> Really? I was sure an algebraic number is any number computable using 
>>> only addition, subtraction, multiplication, division and extraction 
>>> of roots.
>>
>> http://en.wikipedia.org/wiki/Algebraic_number#Numbers_defined_by_radicals
> 
> Right. I think I see what happened here.
> 
> An algebraic number is any number that is the solution to a polynomial 
> equation. And since I thought that all such numbers are constructable by 
> radicals, I assumed "solution of a polynomial" and "constructable by 
> radicals" were equivilent definitions for an algebraic number. 
> Apparently they aren't equivilent. (Which still seems deeply weird to 
> me...)

You'll get used to it soon enough.  I'm sure the result was surprising 
to many people when it came out.  Beautiful bit of math too.

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