> 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.

It's an interesting fact. However, at one point, it occured to me that 
we take radicals for granted as computable. Consider sqrt(2). Somehow, 
we're OK with expressing a number as "the number which, when squared, 
equals two." Yet, we have no way of expressing it otherwise. We've all 
seen approximations to this number, we would recognize it if we saw the 
first few digits, yet we can't actually communicate it without 
describing it in terms of the solution to x*x = 2. (There may be other 
properties it has that we could use to describe it, but we still can't 
just write it down and point to it, like we can with, say, an integer. 
We can never find its precise value, we can only approximate it.)

So, it's kind of interesting that when we can't come up with a way to 
describe a number besides "one of the roots of this degree-5 
polynomial," we typically consider that less descriptive than the value 
of an expression with radicals.

  - Slime

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