Re: Well Ordering the Reals

David Kastrup said:
> Tony Orlow <aeo6@xxxxxxxxxxx> writes:
>
> > Daryl McCullough said:
> >> imaginatorium@xxxxxxxxxxxxx says...
> >>
> >>
> >> >OK, in my right hand I take the subset consisting of the whole set in
> >> >my right hand. Which element should I take in my left hand that is
> >> >mapped to the subset in my right hand?
> >>
> >> Surely you know how the conversation will go from here:
> >>
> >> Tony: You map the largest element in the set to the entire set.
> >> You: But there is no largest element!
> >> Tony: Then why did you bring it up?
> >> You: I didn't bring it up, you did.
> >> Tony: You asked what element gets mapped to the entire set.
> >> Clearly, the answer is "the largest element". So you brought
> >> up the largest element. If you don't want to talk about the
> >> largest element, then don't bring up the largest subset.
> >
> > Perhaps it would go something like that. The basic problem here is
> > that you think of the set as some static well-defined thing,
>
> Which it is.
>
> > and yet, you note that there is no end to it.
>
> Which is perfectly true _because_ of its definition. No "yet" here.
>
> > You cannot name any largest element and therefore cannot name the
> > end of the set
>
> Correct.
>
> > or its true size,
>
> Wrong. You are laboring under the delusion that size requires an
> end. But one can also compare unending entities, by making sure they
> can be matched with other unending entities.
>
> An "end" is the mark of finite sets. We are not talking about those
> here.
>
> > but in speaking about the power set, you treat the set as if it had
> > a static size
>
> Yes.
>
> > and an end,
>
> Wrong.
>
> > when you ask about a mapping to the whole entire set. It really
> > seems like a "last element" contradiction to me.
>
> You just can't get over the fact that sets may have no end.
>
>
If a set has no end, then asking what the mapping to its last element is makes
no sense. Of course you're going to get a contradiction. We have a saying in
the computer industry: garbage in, garbage out.
--
Smiles,

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

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