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Re: Mathematics in brief
Posted:
Dec 9, 2012 4:16 PM
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On 9 Dez., 20:47, Zuhair <zaljo...@gmail.com> wrote:
> On Dec 9, 9:45 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
> > You believe in undefinable numbers. But what should that belief be
> > good for??? We can believe anything we like of undefinable numbers
> > like of unicorns.
>
> No you cannot of course. If you are working within the intended model
> of say Z, then you cannot believe for example that there are finitely
> many undefinable numbers, nor you can believe that there are countably
> many of them, also just because there is no parameter free finitary
> formula after which a number is defined this doesn't mean that you
> lose the known properties of the reals like trichotomy, total
> ordering, etc...
If you don't know what x is, because x is completely undefined, then
you cannot know whether x is positive or negative. Hence there is no
trichotomy with respect to 0. Further you cannot know where x lies in
the order.
Regrads, WM
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