Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 3, 2013 4:13 PM
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In article
<be5cf5d4-da59-46b4-ab5f-3425e8071395@d11g2000yqe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 3 Feb., 09:26, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 3, 8:51 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> >
> > > In fact we can say that in a suitable list "every" initial segment of
> > > s is contained in some line, since there is no s(n) = (s1, s2, ...,
> > > sn) missing. But there is no sensible way of saying "all" initial
> > > segment.
> >
> > We can say "every line has the property that it
> > does not contain every initial segment of segment of s"
> > There is no need to use the concept "all".
>
> Yes, and this is the only sensible way to treat infinity. But "every
> initial segment" has, inadvertently and only noticed by sharp minds
> like those of Brouwer and Weyl, changed into "all initial segments" as
> you can see from the question concerning the path of 1/3 in a Binary
> Tree that contains only every initial segment of the path of 1/3.
If it is actually a path in a CIBT, meaning that it has an actual
inifinity of nodes, then it contains not only every but also all finite
initial segments of the binary form of 1/3
>
> Set theory exists only because of the continued switching between
> these two meanings. If I ask for a level omega distinguishing between
> "every finite path" and the "actually infinite path", I am railed at
> (with full right - a level omega is nonsense). But by sending terms of
> a sequence only, information about an infinite sequence has never been
> transferred.
If one gives a general form for those terms, one defines ALL of them
In binary, 1/3 is 0.(01), where (01) indicates the infinite string of 01
repeating forever.
And every of actually infinitely many proper fractions has has some
finitely expressible binary expression.
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