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.
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.