 #1
Buzz Bloom
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Main Question or Discussion Point
I became curious about the following problem from a discussion in another thread:
After a bit of study I concluded that the meaning of the assertion below regarding some specific real number rl P has the meaning which follows it.
The article
contains the following text:
My QUESTION IS:
Any help would be much appreciated.
After a bit of study I concluded that the meaning of the assertion below regarding some specific real number rl P has the meaning which follows it.
Assertion: "r is not expressible in terms of radicals."
Meaning: r is not expressible in terms of a finite application of a collection of operators (+, , ×, and /, together with any of the nth roots (where n a positive integer) ), where these operators are applied to integer operands, or to expressions of the same kind.
If this meaning is incorrect, I hope someone will correct it.Meaning: r is not expressible in terms of a finite application of a collection of operators (+, , ×, and /, together with any of the nth roots (where n a positive integer) ), where these operators are applied to integer operands, or to expressions of the same kind.
The article
contains the following text:
An example of a quintic whose roots cannot be expressed in terms of radicals is x^{5} − x + 1 = 0.
This simple example of a BringJerrard quintic equation has one real root, with an approximate value ofr = 1.16730397783.
This can be seen in the attached PNG file.My QUESTION IS:
What would a proof that "r is not expressible in terms of radicals" look like?
I have no idea whatever how one would go about proving the nonradical nature of just this one example.Any help would be much appreciated.
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