Re: JSH:Understanding constant terms

From: James Harris (jstevh_at_msn.com)
Date: 11/29/04 

Date: 28 Nov 2004 16:09:33 -0800

"Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message news:<87llcmoxk6.fsf@phiwumbda.org>...
> jstevh@msn.com (James Harris) writes:
>
> > rupertmccallum@yahoo.com (Rupert) wrote in message news:<d6af759.0411271657.2876eeae@posting.google.com>...
> >>
> >> Just because the factors are divisible by 7 when x=0, it doesn't
> >> follow that the factors are divisible by 7 for all values of x.
> >>
> >> <snip>
> >
> > It follows from the distributive property.
> >
>
> Care to step through that argument for us slowpokes?

Sure.

The factor g_1(x) has *two* parts, where one of them is the constant
term, which is constant as it is in fact, 7, and 7 is constant.

The other varies as x varies.

Now the constant term goes from 7 to 1, which means that it is divided
by 7.

Understand?

Well then, by the distributive property, the other term must be
divided by 7 as well, as if you have two parts, then you can't get to
one without going through the other.

For example to help you understand the concept consider

z = x + 7

versus

z/7 = x/7 + 1

and notice that by the distributive property, you can't divide 7 from
the second piece without going through the first!

That's how the distributive property applies.

For other readers, note that I can give detail as necessary with the
argument, and also notice the *level* of detail that posters wish to
request!

That makes the argument in my original post one of the most worked out
in math history with a level of detail that few ever bother to try in
today's math world.

It is a perfect argument, in every detail, as a proof must be.

James Harris

Relevant Pages

  • Re: JSH:Understanding constant terms
    ... > The other varies as x varies. ... > and notice that by the distributive property, you can't divide 7 from ... > in math history with a level of detail that few ever bother to try in ...
    (sci.math)
  • Re: JSH: Point of logic
    ... jstevh@msn.com (James Harris) writes: ... >> How does this follow from the distributive property? ... >> If I told you that x is divisible by w (in some fixed ring R) and ... admission that my math arguments showing the core error in mathematics ...
    (sci.math)
  • Re: JSH:Understanding constant terms
    ... jstevh@msn.com (James Harris) writes: ... I don't see how you're appealing to the distributive property here. ... "I have to break the code of how [mere humans] work, ...
    (sci.math)
  • Re: JSH:Understanding constant terms
    ... James Harris wrote: ... > and notice that by the distributive property, you can't divide 7 from ... and obviously true by the distributive law, ...
    (sci.math)
  • Re: JSH:Understanding constant terms
    ... jstevh@msn.com (James Harris) writes: ... > It follows from the distributive property. ... Care to step through that argument for us slowpokes? ... -- The poetry of Bad Livers ...
    (sci.math)