Re: Well Ordering the Reals
- From: "David R Tribble" <david@xxxxxxxxxxx>
- Date: 1 Dec 2005 10:43:29 -0800
Albrecht Storz wrote:
>> How do you prove, if an object (or a thing which is depicted by a noun)
>> is able to be an element of a set? How do you proof the elementness of
>> objects?
>
David R Tribble wrote:
>> We define a universe that contains "objects" (whatever they are) and
>> also define the existence of "sets" containing zero or more of those
>> objects within that universe. Thus for a given set S in that universe,
>> a given object x is either a member of S or it is not.
>
Albrecht Storz wrote:
> That's not consistent. If so there has to be a set notS which containes
> all x which are not members of S. And then, S union notS has also to be
> a set. But here is no set of all.
The union of S and not S would be all the objects in the universe
that are members of S and those that are not members of S, as well
as set S and all the sets that are not S. The union is therefore
exactly the universe of objects and sets, which is a class, not a set.
.
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