Re: Well Ordering the Reals

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. When I say 1:000...000 is N, that colon is a digital point at
log2(N). 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
to Brian, I haven't figured out all the details, since it doesn't seem like the
most interesting aspect of this stuff, but I guess it's necessary for the
package, so I'll get to tightening it up at some point.
--
Smiles,

Tony
http://www.people.cornell.edu/pages/aeo6/WellOrder/
.

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