Warp wrote:

>   More info on that subject:
> 
> http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

Hmm, interesting. I thought the theorum states that there is no single 
formula that covers all possible polynomials of a given degree. However, 
Wikipedia asserts something far stronger: It seems to claim that you can 
construct a single, fixed polynomial who's solutions (which are also 
fixed) cannot be expressed by radicals.

This indicates that there are some algebraic numbers that are not 
expressible by radicals. (And yet, the *definition* of an algebraic 
number is one expressible by radicals...)

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