Re: Well Ordering the Reals


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?

>When I say 1:000...000 is N, that colon is a digital point at log2(N).

So how far is the last 0 in 1:000...000 from the digital point?


>If I say the point is at N, then I have 2^N as a value. If I say the
> point is at log2(N), and have 1:111...111.111...111, I have 10N/9. Like I said


In 1:111...111.111...111 Do the ellipses represent finite or infinite
gaps?


how far is the forth 1 from the digital point?
how far is the fifth 1 from the digital point?
how far is the seventh 1 from the digital point?
how far is the last 1 from the digital point?

-William Hughes

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