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Virgil

Posts: 8,833
Registered: 1/6/11

Re: Matheology 203
Posted: Feb 6, 2013 4:16 PM

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In article
<c0bf26e7-67c7-4ba5-9688-6374fefd4f48@ia3g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 6 Feb., 17:41, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>
> > > Unlike WM? Did I deny that???
> >
> > You inserted in the quote "{{eg numbers like 0.9999...}}", which is
> > seriously misleading.
>
> Sorry. But it is a well known fact that for every finite period there
> is a base in which this period can be expressed as a single symbol.
> >
> > Thus your quote in no way contradicts Ralf Bader's observation --
> > Brouwer in no way supports your claim that "There is no sensible way of
> > saying that 0.111... is more than every FIS".
> >
> > In fact Brouwer says the opposite here -- 0.1111... is created,
> > and it is *distinct* from any finite sequence.
>
> It is distinct, but it is not definable by creating it. Simply *try*
> it. You must fail. Brouwer has been bisased by the general opinion
> that 0.111... in fact is an infinite sequence. Nevertheless it is
> wrong. But it has lasted several years until I have recognized it.
> Let's see how long it will take you.

At least twice as long as it will take to get parallel lines to meet.
> >
> > > Of course. That's why no uncoutable sets exist.

But that only holds in WMytheology. And Brouwer doesn't live there.
> >
> > Brouwer did not believe that all infinte sets are countable --
> > your claims in that direction are simply false.
>
> I don't know what Brouwer believed. I know what he wrote: Cantor's 2nd
> number class does not exist.
> >
> > >> And in van Dalen, p 118, a letter from Brouwer summarising his thesis:
> > >> "I can formulate:
> > >> 1. Actual infinite sets can be created mathematically, even
> > >> though in the practical applications of mathematics in the world
> > >> only finite sets exist."
> >
> > > Brouwer obviously had not the correct understanding of what actual
> > > infinity is, at least when writing that letter. Errare humanum est.
> >
> > I venture to suggest that Brouwer had a better grasp
> > of these matters than yourself.
>
> Maybe. But may also be that you have not a good grasp of his grasp.

But Alan's grasp of Brouwer is still both finitely and infinitely better
than WM's.
>
> Regards, WM
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