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jstevh@xxxxxxx wrote:
> David Bernier wrote:
> > jstevh@xxxxxxx wrote:
> >
> > [...]
> >
> > > What if here you betrayed humanity and condemned it?
> >
> > What if Gaussian integers fail "full coverage"?
> >
> > David Bernier
>
> Good question.
>
> They don't.
>
> The simplest example is still the one that covers the major issue as
> consider evens as a ring and then 2 is coprime to 6, because 3 is NOT
> even.
But this is because silly mathematicians made a mistake when
they defined the evens to be the numbers that were divisible
by 2.
>
> You can find a problem very similar to that with the ring of algebraic
> integers where you get a "coprime" result where algebraically it's
> meaningless, but you can't with the gaussian integers.
>
> My point is that certain numbers are excluded from the ring of
> algebraic integers just because they cannot be roots of monic
> polynomials with integer coefficients, just like 3 is excluded from
> evens because it's not even.
>
> Past mathematicians never realized that all exclusion from the ring of
> algebraic integers means is that a number is not the root of some monic
> polynomial with integer coefficients--and nothing else.
>
> Because they stepped too far--beyond what mathematical logic
> supports--they came up with "proofs" that are not mathematical proofs,
> which ultimately just prove--that a particular number is not the root
> of some monic polynomial with integer coefficients.
>
> BUT because they didn't realize their error and a lot of mathematical
> ideas were built on top of the error, all those ideas fail, which is a
> political thing as well, so just like George W. Bush and his cronies
> will not admit error, neither will Barry Mazur and his.
>
>
> James Harris
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