In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 24 Mrz., 01:41, Virgil <vir...@ligriv.com> wrote: > > In article > > <5c674f26-92a7-44ed-b080-692d23ec3...@g4g2000yqd.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > Do you think it is not a contradiction, to have the statements: > > > 1) 0.111... has more 1's than any finite sequence of 1's. > > > 2) But if we remove all finite sequences of 1's, then nothing remains. > > > > In proper English (1) should read > > "the infinite sequence represented by 0.111... has more 1's in it > > than in any finite sequence of 1's." > > You seem to have difficulties when terminology of proper mathematics > is in question. 0.111... is an infinite sequence that represents a > number - it is not only representing an infinite sequence.
But it is false to say that as a string of characters it contains any more than 3 "1"'s. > > > > And if WM wishes to prevail, he WM must explain how he intends to remove > > all finite sequences of 1's without removing all 1's in the process. > > That is simple: All finite sequences like > 0.1 > 0.11 > 0.111 > ... > can be removed from 1/9 without ever removing all.
1/9 names a number, and that number is just a number and not either a finite nor an infinite sequence, though some of its other names are.
The finite sequences "0.1" "0.11" "0.111" and others may be removed from the infinite sequence abbreviated by "0.111..."
> So, if 1/9 has a > decimal representation > > > > The fact is that one cannot remove every set containing a natural from a > > family of sets some of which contain that natural of without removing > > that natural from the union of set of remaining sets. > > of without removing? Proper English?
My error, which apparently did not make my statement any less understandable. > > > I proved that every FISON and all its predecessors can be removed from > the matheological union |N of all FISONs without changing this union.
ANY FISON and all its predecessors can be removed from the union |N of all FISONs without changing this union.
But removing every FISON leaves none to form a union.
> Everybody with a minimum of mathematical knowledge can do so by > himself or can at least understand my proof.
We all understand that it is wrong to say, ss WM is doing here, that one can remove everything and still have something left, at least wrong everywhere except in Wolkenmuekenheim. > > Regards, WM --