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Topic: Matheology 203
Replies: 3   Last Post: Feb 6, 2013 4:06 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: WMytheology 203
Posted: Feb 6, 2013 4:06 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 6 Feb., 13:32, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 6 Feb., 04:47, Ralf Bader <ba...@nefkom.net> wrote:
> > >> According to Mückenheim, "There is no
> > >> sensible way of saying that 0.111... is more than every
> > >> FIS". Of the authorities you called upon, whom would you find capable of
> > >> regardng this as a sensible assertion

> >
> > > Compare Matheology § 030:   We can create in mathematics nothing but
> > > finite sequences, and further, on the ground of the clearly conceived
> > > "and so on", the order type omega, but only consisting of equal
> > > elements {{i.e. numbers like 0,999...}}, so that we can never imagine
> > > the arbitrary infinite binary fractions as finished {{Brouwers Thesis,
> > > p. 143}}. [Dirk van Dalen: "Mystic, Geometer, and Intuitionist: The
> > > Life of L.E.J. Brouwer", Oxford University Press (2002)]

> >
> > van Dalen, unlike WM, is careful to note Brouwer's own note
> > on "equal elements":
> >
> >    "Where one says 'and so on', one means the arbitrary
> >     repetition of the same thing or operation, even though that thing or
> >     operation may be defined in a complex way"
> >
> > thus justifying existence of expansions like 0.12121212...

>
> Unlike WM? Did I deny that??? Of course even the existence of 0.
> [142857] and every other periodic decimal fraction is possible
> according to Brouwer. If you can't believe that this is covered by my
> § 030, then simply use the septimal system even if it is not an
> optimal system.

> >
> > "arbitrary" sequences are a different matter.

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

Thus ins WM's mind, everyone but WM is wrong!
>
> Just a question: Have you ever seen a Cantor-list where more than half
> of the interesting sequences (a_j) of digits a_kj with k < j had
> infinite length? Have you ever seen a Cantor-list with at least one of
> the interesting sequences of digits having infinite length? No? Why
> the heck do you believe that they play the crucial role in Cantor's
> "proof"?

Any finite sequence can be infinitely extended by zeros, at lest in
Brouwer's world, so that any sequence of finite sequnces is also a
sequence of infinite sequences, and Brouwer disproves WMytheology.

>
> Try to imagine this "proof" without the obviously counterfactual
> belief that irrelevant tails beyond a_jj play any role. What remains?
>
> Regards, WM

--

Date Subject Author
2/6/13 Alan Smaill
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil