In article <2ba92cba-9945-4843-b15e-c39749705827@d10g2000vbk.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 6 Dez., 03:28, William Hughes <wpihug...@gmail.com> wrote: > > On Dec 5, 3:47 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 5 Dez., 04:17, Daryl McCullough <stevendaryl3...@yahoo.com> wrote: > > > > > > On Sunday, December 4, 2011 4:10:29 PM UTC-5, WM wrote: > > > > > > But there is no reason to believe it is true for the set of ALL > > > > > > FISONs. In particular, the statement: > > > > > > > > The union of any collection of FISONs is another FISON. > > > > > > > > is false, > > > > > > > That is a statement of belief. > > > > > > No, it's provable. > > > > > The contrary is provable too. > > > > > I am talking about the *sequence* of sets of exponents of (a_k) with > > > a_k = 10^-1 + 10^-2 + ... + 10^-k. > > > > > This sequence (without its limit) contains all natural numbers. Every > > > set contains all natural numbers that are contained in the preceding > > > sets. The sequence does not contain an infinite set. So every set is a > > > FISON. > > > > Every element of A={a_k|k in N} is a FISON. > > Look! Over There! A Pink Elephant! > > No elephant required. > Here we have not the hocus-pokus of set unions. Here we have finite > mathematics with finite sets (FISONs). And there do no two or > infinitely many different FISONs exit, that contain more natural > numbers than each of them. No.
> All natural numbers that exist are in a > FISON.
Do you mean for each natural there is a fison that it is in or there is some fison that every natural number is in ?
Careful not to let your quantifier dyslexia fool you again in answering!
> There is no last number and there is no last FISON.
That means that both sequnces are infinite sequences.
Indeed, for the JvN naturals, they are the same infinite sequence!
> But what's > there is there without matheological distribution problems.
You are in charge of what goes on in mathelogy. We mere mathematicians have no authority there.
> Perhaps you believe: > Look! Over There! A Pink Elephant! > There fit aleph_0 numbers into one FISON.
No, but we do believe that there are aleph_0 naturals that fit into the union of all fisons.
> > I do not believe that and do not accept that as meaningful > mathematics.
Elsewhere you have claimed that to cover all naturals only one fison is needed, whereas standard mathematics claims that no finite set of fisons can cover all naturals but any and every infinite set of fisons does. --
