Re: Well Ordering the Reals

In article <MPG.1de6898d71a0a88a98a71f@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> imaginatorium@xxxxxxxxxxxxx said:
> >
> > Tony Orlow wrote:
> > > Virgil said:
> > > > In article
> > > > <MPG.1de5394567f6ae1998a712@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > > Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> > > >
> > > > > David R Tribble said:
> > > >
> > > > > > If your N and 2^N-1 were really different (infinite)
> > > > > > numbers, then your ...111(2) and your "unit infinity" also
> > > > > > must be different numbers.
> > > > > They are. N=1:000...000. ....1111 might be considered a
> > > > > poorly formed version of N-1, but one really can't tell how
> > > > > that relates to 1:000...000. I am not sure why you say this
> > > > > anyway.
> > > >
> > > >
> > > > TO posits a seqeuence starting with an infinite sequence of 0's
> > > > and ending with an reversed infinite sequence of zeros, which
> > > > he denotes by 000...000.
> > > Yes, it is an "uncountably" infinite string of 0's.
> >
> > What is your (TO) definition of "uncountably" (or of
> > '"uncountably"' if you like)? I think that it is pretty much a
> > defining characteristic of any uncountably infinite set in normal
> > maths that it cannot be arranged in a sequence. Isn't that what
> > "string" implies? That each one of these 0's is followed by a next
> > one, and so on? (I confess I'm not paying _that_ much attention,
> > and I'm not too sure what this string is, but never mind.)
> >
> > Brian Chandler http://imaginatorium.org
> >
> >
> Actually inifnite, such that there are bits that are infinitely
> distant from each other.


Then there can only be finitely many points on any circle or in any
bounded real interval.


> Seeing as I don't see a real successorship problem in going from
> finite naturals to infinite naturals in infinite setps, the concept
> of such an infinite sequence doesn't cause a problem for me.

The collection of anomalies and contradictions in TO's assumptions that
TO chooses not to see may well be itself uncountable.
.

Relevant Pages

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