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


Re: WMytheology 203
Posted:
Feb 6, 2013 4:06 PM


In article <12b0ec4a58194a36a5d87f6adf5bcb3d@z9g2000vbx.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 6 Feb., 13:32, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: > > WM <mueck...@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... > > 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 Cantorlist 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 Cantorlist 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 



