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


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



