Date: Feb 6, 2013 7:32 AM
Author: Alan Smaill
Subject: Re: Matheology 203
WM <mueckenh@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...

"arbitrary" sequences are a different matter.

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."

> Regards, WM

--

Alan Smaill