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Re: Matheology § 214
Posted:
Feb 11, 2013 4:07 AM
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On 11 Feb., 09:55, fom <fomJ...@nyms.net> wrote:
> On 2/11/2013 2:43 AM, WM wrote:
>
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> > On 11 Feb., 08:48, Virgil <vir...@ligriv.com> wrote:
> >> In article
> >> <b96a20cb-7991-4a49-84ca-6bd658501...@w7g2000yqo.googlegroups.com>,
> >> WM <mueck...@rz.fh-augsburg.de> wrote:
>
> >>>> Every potentially infinite set already exists.
>
> >>> But none of them are, or ever can become, infinite.
>
> > They cannot "become" actually infinite.
>
> >> Since such "sets" are neither finite nor not finite (infinite), they are
> >> nonexistent.
>
> >> And in van Dalen, p 118, a letter from Brouwer summarising his thesis:
> >> "I can formulate:
> >> 1. Actual infinite sets can be created mathematically"
>
> > As I already mentioned, that is due to an understandable error. At
> > that time mathematicians were drilled to understand by the finite
> > expression "0.111..." an actually infinite sequence of digits. That is
> > wrong.
>
> Right and wrong....
>
> What, in modern mathematics, happened to change that
> situation?
I am teaching my contemporaries. Some have already understood. But it
is a hard job because mathematicians are very, hmm, say conservative.
Regards, WM
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