Re: Well Ordering the Reals

Virgil said:
> In article <MPG.1df92539b90a515d98a7dd@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
>
> > David R Tribble said:
> > > Tony Orlow wrote:
> > > >> 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).
> > > >
> > >
> > > William Hughes wrote:
> > > > What is a your definition of a finite neighborhood? So how far is
> > > > the last 0 in 1:000...000 from the digital point?
> > >
> > > More questions for Tony: When you write x = 0:100...000, and you
> > > say that the "..." represents an infinite number of zero bits, you
> > > appear to be definining a number with an infinite number of low
> > > zero bits "...000" and three extra high bits "100" positioned past
> > > the last infinitely-positioned low zero bit.
> > >
> > > It looks x is composed of oo+3 bits. Or does the "..." represent
> > > only oo-3 bits? What is 3 bits shy of infinity?
> >
> > Another infinite number, but I think you are misunderstanding. When I
> > say 1:000...000 is N and has log2(N) digits, I mean the 0's, not the
> > 1. The whole string between the 0 point and the log2(N) point is
> > log2(N) bits.
>
> But starting at the leftmost 0 of 1:000...000 one can count off N zeros
> to the right, and counting from the rightmost 0, one can count off N
> zeros to the left without ever overlapping or covering the same ground,
> so that in TO's arithmetic, log2(N) must satisfy log2(N) >= N + N.

What are you on? There are log2(N) bits there. You are thinking N is some
countable infinity. It's not. Your objections are like me insisting that log2
(N) and N have different "cardinalities", which they don't. They have different
"bigulosities". Virgilogic doesn't apply here.

>
> I must say that I prefer standard arithmetic to the odiocies of TO's
> T-errible number system.

Of course you prefer to think what you already think, because you're an
intellectual stick in the mud. Or, is that even mud? Just keep that end away
from me. I can smell it from here.

>

--
Smiles,

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

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