Date: Mar 24, 2013 5:08 AM
Subject: Re: Matheology § 224
On 24 Mrz., 01:41, Virgil <vir...@ligriv.com> wrote:
> In article
> 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
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.