Re: Well Ordering the Reals

In article <MPG.1dfa8312b8880bdb98a80d@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:


> > So that the "limit points" must form a dense subset of the set of
> > T-errible numbers having between any two "limit points" another
> > "limit point"!

> Sort of, to a point. Any infinite distance between points can always
> be divided in two for two infinite distances. So, one can have a
> countably infinite set between any two. That is, one can divide an
> infinite distance any finite number of times and still have an
> infinite distance. But this does not make the set of limit points
> dense on the finite scale. They are still infinitely far apart.

Density is not a matter of scale. An ordered set is dense if and only if
between any two members there is another member.
> > > >
> > > > TO's whole T-errible system is really terrible.
> >
> > > Why do you say that? I have answered every question you've posed
> >
> > TO has evaded almost every question, rather than answering it, and
> > has ignored all the anomalies his "system" creates.
> I answer all your questions, just not all the repetitions of them.

Here is one more question: Imagine a "TO-number" with zeros from its
left end rightward to the furthest extent covered by some known internal
"limit point', and all 1's from there on rightward. What is its
successor?
> >
> >
> > > What is it you hate so much about me or my ideas? Is it just
> > > because I smell like a cat?
> >
> > I am quite fond of most cats. But ideas that are self-contradictory
> > and people who try to sell them I am not fond of.
.

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