Re: JSH: Inconsistency with algebraic integers

On May 25, 4:41 pm, marcus_b <marcus_bruck...@xxxxxxxxx> wrote:
On May 25, 4:25 pm, jst...@xxxxxxxxx wrote:

Now at least it is possible to carefully explain exactly what is wrong
with the ring of algebraic integers as using it you can appear to
prove two different and opposite things.

So I can start with an identity, the factorization:

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

That's not an identity, because at this stage - the starting
stage - you have not defined f(x) or g(x). An identity is
something like

x^2 - 1 = (x + 1)*(x - 1),

which is true regardless of what number x is. But

175x^2 - 15 x + 2 = (f(x)+2)(g(x)+1)

is not true for all possible definitions of f(x) and g(x); it
is not an identity.


ALL factorizations are identities.


James Harris

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