Re: Well Ordering the Reals

In article <MPG.1df90761c0d9d7b98a7d1@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> William Hughes said:
> >
> > Tony Orlow wrote:
> > > Matt Gutting said:
> > > > >> BINGO! The whole question is "what is this additional
> > > > >> specification"
> > > > > The places of the bits, either relative or absolute.
> > > >
> > > > You're arguing circularly. "The places of the bits, either
> > > > relative or absolute" must be determined by some indexing set.
> > > > "The places of the bits" are precisely what determines
> > > > "whichever is to the left of the other". But that's precisely
> > > > what we're asking.
> > > >
> > >
> > > Okay, sure. I just said this in another post, that as I think
> > > about it now, it seems that the general approach is essentially
> > > to define multiple digital points. With normal finite digital
> > > numbers, all significant digits are within a finite number of
> > > steps of THE digital point at bit 0, and that's how we know their
> > > values. I guess what my system really boils down to is defining
> > > multiple digital points, at locations infinitely far apart in the
> > > string, with finite neighborhoods.
> >
> > What is a your definition of a finite neighborhood?
> The set of points within a finite number of bit positions of a
> "limit" digital point, such as 0 or log2(N).

So that TO is trying to "well order" his set of digit positions in some
weird way?

His difficulty will be how to deal with a that the "carry" operation
that carries out of the neighborhood of one of his "limit" digital
points and into the neighbor hood of another.

For instance, given any one of these "limit" digital points, how does
one determine what the next one will be? There has to be a next one,
doesn't there?

And the indexing within each neighborhood will have to correspond to
being indexed by the set of all finite integers, 0 at the "imit"
position, positive for more significant and negative for less.

And here is always the vexing problem of how does the transition from
one such "neighborhood" to the next work?
.

Relevant Pages

  • Re: Wal-Mart now has steaks
    ... We have a lovely butcher shop in our neighborhood. ... Well, okay, a ... meat-cutter, but they know the source of all the meat they sell, and I can ...
    (rec.food.cooking)
  • Re: Wal-Mart now has steaks
    ... We have a lovely butcher shop in our neighborhood. ... Well, okay, a meat-cutter, but they know the source of all the meat they sell, and I can get any cut I want. ...
    (rec.food.cooking)
  • Re: El Pollo Loco Judged...
    ... A bit dry, but better than KGC. ... The sides were okay. ... name in your neighborhood. ...
    (rec.sport.football.college)
  • Re: TV MEs
    ... My favorite is in the neighborhood. ... Louie Sanchez ... (okay, Luis Sanchez, M.D.) ...
    (rec.arts.mystery)
Loading