On 8 Dez., 10:04, Virgil <vir...@ligriv.com> wrote: > In article > <1b1366e9-3275-4774-89e0-ba9c556cc...@t16g2000vba.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 8 Dez., 00:54, William Hughes <wpihug...@gmail.com> wrote: > > > On Dec 7, 5:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > There is no collapse required. The sets are constructed such that each > > successor contains all contents of its predecessors. > > > This is so by definition. If you doubt that this definition is > > satisfied by the sequence 0.1, 0.11, 0.111, ..., then you have to > > prove this > > The "set" 0.11 does not contain the "set" 0.1 as a subset because > neither of them is a set, at least not in normal mathematics.
O how right you are. But as you know well enough, this is only the abbreviation for the sequence of FISONs that is obtained from the indices of the digits 1 or the exponents of the powers of 10 in the numbers. Do you really think it is necessary, to argue in this way? Then you seem to have no useful arguments.
> , but by finite mathematics. In finite mathematics we proceed by > > > showing a counter example. In finite mathematics (my proof belongs to > > that realm because every FISON is finite (!)) we need a finite counter > > example. That requires, in the present case, to find two FISONs A, B > > that are necessary: > > E a,b in |N, A,B in S: (a in A & b ~in A) & (b in B & a ~in B). > > Unless you can show such a pair of FISONs your argument is null and > > void in mathematics. > > Nope! while of any two fisons, one is a proper subset of the other, > there is no fison of which all others are proper subsets.
That is matheology and strongly depends on what we understand by "all". But we can be sure, that there are not more natural numbers than are in one and the same FISON of the sequence. > > PROOF: Any such fison, S_k, alleged to contain all other fisons, S_j's, > as subsets fails to contain its successor fison S_(k+1) as a subset. > And every fison, like every natural, has a succesor.
If a theory supplies two proofs that contradict each other, then the theory is useless. This is the case with a theory that results in finished infinity. Therefore I recommend: Please ty to remember how you learned and applied mathematics before you fell into the traps of matheology.