On 3/24/2013 4:08 AM, WM 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.
You are repeatedly asked for proper definitions of your use of terms in statements. That is what proper mathematics dictates.
> 0.111... is an infinite sequence that represents a > number
Well, the not-so-finite finite reappears. WM is the sometimes ultrafinitist, who is always assuming infinity.
>- it is not only representing an infinite sequence.
That is why proper definitions are needed.
All '0.111...' in these discussions is that no one can take away your crayons. No definition. No intelligible meaning.
>> >> 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.
That's an assertion.
He asked for explanation.
Please provide that which had been requested.
> So, if 1/9 has a > decimal representation, something must remain, nat least the > counterfactual belief of matheologians. >>
Told you before -- mathematics does not deal with the truth conditions of counterfactuals. The only arguing from belief here is you.
>> 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?
The occasional typographic error is far more decipherable than your theory of monotonic inclusive crayon marks.
>> > I proved
You have *proven* nothing.
Once again, the only thing close to *proof* with which you may be associated is the result of WH's patient attempts to discern anything close to rational from your remarks.