Re: Proposal: 6NF
Date: 21 Oct 2006 18:49:11 -0700
Message-ID: <1161481751.611885.234750_at_i3g2000cwc.googlegroups.com>
Christopher Browne wrote:
> Quoth "Keith H Duggar" <duggar_at_alum.mit.edu>:
> > vc wrote:
> > > Marshall wrote:
> > > > I do not recall learning anything in secondary school
> > > > which would suggest 2 and 2.0 were numerically different
> > > > in any way. Nor can I think of any *arithmetic* way to
> > > > distinguish between 2 and 2.0.
> > >
> > > You have to construct all the real numbers and prove
> > > that 2 is an element of the set.
> >
> > Any mathematical number construct that fails to equate
> > 2.0 and 2, fails to model our most basic common sense or
> > "elemntary school" concept of the number 2.
>
> In abstract algebra, you get groups and other structures where
> 2 may be a meaningful value, but 2.0 isn't
> because there isn't any inherent notion of fractional values.
> Indeed, in the realm of discrete mathematics, it's
> [meaningless] (even undesirable!) to have any values lying
> between 1 and 2 and 2 and 3.
>
> Proof by induction, for instance, depends on the notion that
> there are no intermediate values.
> I don't think that "elemntary school" concepts are of any
> particular relevance when looking at mathematical structures;
> they are what they are, irrespective of whether a layman can
> relate them to anything that seems familiar to the layman.
Certainly I agree there are mathematical structures beyond the comprehension of some or many us. However, the concept of the number 2 or 2.0 is not such a structure.
Keith -- Fraud 6
PS. I really enjoyed reading your post. It was a refreshing
change from C'mode and VC. And, it would be great if you replied
again. I'm particularly interested in what you think regarding
the purpose of mathematics as a human tool.