Re: Well Ordering the Reals

Tony Orlow wrote:
> Daryl McCullough said:
> > Tony Orlow says...
> >
> > >Fine, if you say so, but I can certainly entertain notions of infinite-tuples,
> > >and am not the only one. Perhaps they aren't usually called n-tuples, but for
> > >infinite n, there is no difference. What was your point, anyway?
> >
> > Going back in the thread, I said that in mathematics, a "list" refers
> > to a set of elements indexed by finite natural numbers, and you disputed
> > that. You provided a bunch of URLs that all agreed with my terminology.
> >
> And this was in the context of a well ordering as a list? Well, then, no well
> ordering could ever be performed on an uncountable set, then, could it?

Tony, I wonder if it will occur to you to look up the definition of
"well order" in a book? It is not the same as "enumeration": in
particular (we're told) the axiom of choice implies that every set has
a well-ordering, but a very simple proof shows that there cannot be an
enumeration of the (standard) reals. You are making things rather hard
for yourself by trying to prove the one that is impossible, instead of
the one that should be possible.

Brian Chandler
http://imaginatorium.org

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