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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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