JSH: Factorizations are identities
JSH
mathematics in replies to my previous threads so some points of
reminder:
1. Factorizations are identities!!!
So, like with x^2 + 3x + 2 = (x+1)(x+2), notice the SAME THING on both
sides of the equals!!!
It just looks different one one side. But it's the SAME THING. A
factorization is an identity.
The ring of algebraic integers bizarrely violates a principle in
certain special cases with a special construction, which is equivalent
then to blocking the case that given 7x = 7x, x=x, as it will not
allow you to divide the 7 off.
2. If you do not address the issue properly then you have a
fundamental mathematical contradiction!
So if you just say, no way, no problem is possible here, everything is
ok, then you're also saying: mathematics contradicts!
So you're ultimately trashing all of human mathematics.
Mathematics does not allow shades of gray.
Posters get away with denying mathematics entire by people not
accepting that mathematical logic does not allow you to say it's ok
for the ring of algebraic integers to disobey basic principles of
identity.
If you so allow you end mathematics itself. You declare it to be
inconsistent.
3. The special construction is mathematically irrefutable. It shows
a profound flaw with defining a ring as having only as members the
roots of monic polynomials with integer coefficients.
That's the easy part.
If I were having this discussion with Gauss and Dedekind that would be
it. The demonstration would be enough.
But many of you are ready to toss mathematics entire, and declare it
to be inconsistent today, only because of 100+ years with the error.
Nothing more.
So at the end of the day, protestations of rigor and claim of love of
mathematical truth were tossed by many of you based on time alone.
Time with a massively devastating error, which just happens to show
some people were wrong for over a hundred years.
People have been wrong for longer.
_________________________
7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)
where the a's are roots of
a^2 - (7x-1)a + (49x^2 - 14x) = 0.
That special construction blows apart some flawed ideas. That's all.
To hold on to those flawed ideas you have to dismiss mathematical
consistency itself.
For any of you looking for authority, or looking to authority, you
simply take that construction to your favorite math teacher, and ask
him or her to divide off the 7 in the ring of algebraic integers.
It cannot be done. That ring breaks the identity principle. It grabs
the 7 like a desperate lover--and refuse in general to let go.
A proper ring would not behave in such a way.
James Harris
Rotwang
>
> [...]
>
> 7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)
>
> where the a's are roots of
>
> a^2 - (7x-1)a + (49x^2 - 14x) = 0.
>
> That special construction blows apart some flawed ideas. That's all.
> To hold on to those flawed ideas you have to dismiss mathematical
> consistency itself.
>
> For any of you looking for authority, or looking to authority, you
> simply take that construction to your favorite math teacher, and ask
> him or her to divide off the 7 in the ring of algebraic integers.
>
> It cannot be done. That ring breaks the identity principle. It grabs
> the 7 like a desperate lover--and refuse in general to let go.
>
> A proper ring would not behave in such a way.
And since the object ring is a proper ring, presumably it doesn't
behave in such a way. So...
7*(25x^2 + 5x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)
where the a's are the roots of
a^2 - (x - 1)a + 7x^2 = 0.
Please divide off the 7 in the object ring.