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Topic: § 488 Who said this?
Replies: 187   Last Post: May 7, 2014 10:06 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: § 488 Who said this?
Posted: May 3, 2014 5:39 AM

On Saturday, 3 May 2014 10:25:00 UTC+2, Zeit Geist wrote:
> On Saturday, May 3, 2014 12:48:09 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
>

> > On Friday, 2 May 2014 23:20:55 UTC+2, Zeit Geist wrote:
>
> >
>
> > > Can you please provide a Countable List
>
> >
>
> > Every list is countable.
>
> >
>
> > > of ALL Finitely Definable Real Numbers?
>
> > > Remember, this List must have a Finite Definition.
>
> >
>
> > I use set theory. All finite expressions in all possible (non-formal and formal) languages form a countable set. This is undisputed except by extreme-matheologians who wish to create uncountably many languages or uncountable alphabets. I do not argue with them.
>
> >
>
>
>
> But there are Uncountable many Languages.

As I said, I do not discuss with fools.

> Just pick one.

Impossible without a dictionary. A language has to be known by the user. For that sake there has to be a dictionary. You can costruct it, if you like, but there can never more than a finite number of languages exist.
>
>
>
>

> > A real number is defined by (at least) one or (frequently) more of those expressions. Therefore all real numbers form a subset of the set of all finite expressions. According to ZF set theory a subset of a countable set is countable.
>

>
> But how do you know that that countable subset is Finitely Definable?

I do not know it. I know that every subset of a countable set is countable in ZF.

>
> Give an Explicit Definition of that List.

Why? I show that the assumption of infinite lists, i.e., of bijections with |N, lead to contradictions with the rule that subsets cannot have larger cardinality than sets.

Regards, WM

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4/29/14 mueckenh@rz.fh-augsburg.de
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5/4/14 Dan Christensen
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5/5/14 mueckenh@rz.fh-augsburg.de
5/5/14 Tucsondrew@me.com
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