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. > > 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. So, if 1/9 has a decimal representation, something must remain, nat least the counterfactual belief of matheologians. > > 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? > I proved that every FISON and all its predecessors can be removed from the matheological union |N of all FISONs without changing this union. Everybody with a minimum of mathematical knowledge can do so by himself or can at least understand my proof.