Math Forum Discussions

mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05

Re: Matheology 203
Posted: Feb 6, 2013 2:01 PM

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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.
>
> > Of course. That's why no uncoutable sets exist.
>
> 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.

Regards, WM