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Re: Matheology 203
Posted:
Feb 6, 2013 7:32 AM


WM <mueckenh@rz.fhaugsburg.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



