Date: Mar 3, 2013 4:19 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<cc803d21-3112-4a75-b56b-a4c4ad47a2a3@gp5g2000vbb.googlegroups.com>,
WM <mueckenh@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.
>
> However, in mathematics based upon reality and therefore being
> correct, 2 + 2 = 4.


And 4 = 1 mod 3.

This is just a special form of clock arithmetic, so that if WM cannot do
it, perhaps Wolkenmuekenheim does not allow for clocks.
--