In article <email@example.com>, WM <firstname.lastname@example.org> 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. --