Re: Well-ordering principle

On Tue, 28 Oct 2003 03:10:19 GMT, "Steven Margolin"
<[EMAIL PROTECTED]> wrote:

>
>"David C. Ullrich" <[EMAIL PROTECTED]> wrote in message
>news:[EMAIL PROTECTED]
>> On Mon, 27 Oct 2003 20:00:44 GMT, "Steven Margolin"
>> <[EMAIL PROTECTED]> wrote:
>>
>> >
>> >"David C. Ullrich" <[EMAIL PROTECTED]> wrote in message
>> >news:[EMAIL PROTECTED]
>> >> On Mon, 27 Oct 2003 03:11:38 GMT, "Steven Margolin"
>> >> <[EMAIL PROTECTED]> wrote:
>> >>
>> >> >I have heard that with Choice, the reals are, while still uncountable,
>> >> >well-ordered.  This does not make sense to me.  If they are
>well-ordered,
>> >> >then they can be listed, so what about Cantor's Diaganolization
>Argument?
>> >>
>> >> Somehow you got the idea that well-ordered implies countable. Not so.
>> >I sort of understand that, but the reals, with unique ternary
>> >representations, are uncountable by a number of proofs, and one of them
>is
>> >CDA.  However, with WOP, a roster notation of the reals is possible, so
>take
>> >that roster and list it.  Now, we have a (perhaps uncountable) listing of
>> >the reals, but Cantor says we cannot have that.
>>
>> Huh?????????
>>
>> > For example, with the set
>> >of ordinals, less than w_2, CDA would be meaningless.  Using CDA on a
>> >well-ordering of the reals would likely produce a number that, while in
>the
>> >list, is uncountably far away.
>>
>> You need to explain this much more carefully, otherwise people will
>> assume you're just babbling nonsense when they realize they have
>> no idea what you're talking about.
>You are right, I do I believe that I am talking out my arse, and I think
>that my question was answered about 10 posts ago when someone said that you
>cannot create real number with an uncountable number of digits.

Well I have to say I was surprised to read that. I was expecting this 
thread to start veering towards the dark side... congratulations.

>>
>> >> >I have also heard that you need to able to give a finite number to
>> >> >correspond to any number I name, but this can be solved by putting the
>> >> >definable numbers first.
>> >> >Me Please Explain.
>> >>
>> >> Hard to explain, since I have no idea what the previous paragraph
>> >> means.
>> >> ************************
>> >>
>> >> David C. Ullrich
>> >
>>
>> ************************
>>
>> David C. Ullrich
>

************************

David C. Ullrich