Re: Well Ordering the Reals


David R Tribble wrote:
> Albrecht Storz wrote:
> >> This must hold in the exact same manner for the inexhaustible supply of
> >> natural numbers. Since it's inexhaustible you can't have all of those.
> >> The set N doesn't exist. That's what I'm talking about the whole time.
> >
>
> William Hughes wrote:
> >> No, you cannot get all the numbers from the inexaustible supply.
> >> But what about the entity "the inexaustible supply". Does this
> >> entity not exist?
> >
>
> Albrecht Storz wrote:
> > It's no entity in any useful sense of the word. So it exists, but it is
> > no entity and it is no set. Maybe it's a potential.
>
> All a set has to be is a collection of zero or more elements.
> N is a collection of elements, each of them being a natural
> number. So how is N not a set?

Maybe, if you put infinitely many elements together in a set, the
elements will be squashed together and thereby lose their identity?

If you put out infinitely many elements out of an infinite set, the set
don't change its cardinality. So, if you put out #1, #2, #3, and so on
out of N, N stays like it is. So, perhaps there is no #1, #2, #3, ...,
there is only #infinit, #infinite, #infinite, ... infinitely often in
an infinite set.
???

Regards

Albrecht Storz

.

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