Date: Mar 3, 2013 5:10 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 3 Mrz., 22:19, Virgil <vir...@ligriv.com> wrote:
> In article
> <cc803d21-3112-4a75-b56b-a4c4ad47a...@gp5g2000vbb.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 3 Mrz., 00:00, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <4e4bb67d-abca-470f-a4b0-f5d1681d9...@u2g2000vbx.googlegroups.com>,

>
> > >  WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > On 2 Mrz., 22:55, Virgil <vir...@ligriv.com> wrote:
> > > > > In article
> > > > > <1f6ffc0a-1cf2-41cf-9548-73ed71cde...@u2g2000vbx.googlegroups.com>,

>
> > > > >  WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > > > On 1 Mrz., 22:56, Virgil <vir...@ligriv.com> wrote:
> > > > > > > In article
> > > > > > > <dcc0a841-b24c-4aba-beac-1358c7692...@h11g2000vbf.googlegroups.com>,

>
> > > > > > >  WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > > > > > On 28 Feb., 22:14, Virgil <vir...@ligriv.com> wrote:
>
> > > > > > > > > WM confuses those names with the things named.
>
> > > > > > > > No.
>
> > > > > > > > > One, two three, and so on, are names .
>
> > > > > > > > > Ein, Zwei, Drei, und so weiter, are different names but name
> > > > > > > > > the
> > > > > > > > > same
> > > > > > > > > things.

>
> > > > > > > > There are rules according to which different names can be put
> > > > > > > > together
> > > > > > > > to form sentences. These rules belong to mathematics.

>
> > > > > > > For the English language such rules belong to the grammar of the
> > > > > > > entire
> > > > > > > language, not merely to mathematics

>
> > > > > > The rule that 2 + 2 can be replaced by 4 belongs to the grammer of
> > > > > > English language?

>
> > > > > The rule that 2 + 2 can be replaced by 4, at least in many contexts, is
> > > > > certainly compatible with the rules of English grammmar.
> > > > > Is it not compatible with German grammar?

>
> > > > Don't mistake being compatible with being forced.
>
> > > 2 + 2 is not forced to be equal to 4 in English, because in the field of
> > > integers mod 3, only 0, 1 and 2 occur, no 4 occurs, but 2 + 2 still does
> > > and results in 1.

>
> > So your integers form a field?
>
> The integers 0,1 and 2 can form a field if the arithmetic is that of
> integers modulo 3.
>
> Note that whether a set of objects forms a field or not depends only on
> how the relevant operations of addition and multiplication are defined
> on the objects of that set, not on what the members of that set are in
> other contexts.


And the multiplicative inverse is not required?
Ever heard of a ring without rang and rung?

Regards, WM