In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 15 Mrz., 17:13, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 14, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > <snip> > > > > > > > > > > > > >... consider the list of finite initial segments of natural numbers > > > > > 1 > > > 1, 2 > > > 1, 2, 3 > > > ... > > > > > According to set theory it contains all aleph_0 natural numbers in its > > > lines. But is does not contain a line containing all natural numbers. > > > Therefore it must be claimed that more than one line is required to > > > contain all natural numbers. This means at least two line are > > > necessary. There are no special lines necessary, but there must be at > > > least two. In this case, however, we can prove, by the construction of > > > the list, that every union of a pair of lines is contained in one of > > > the lines. This contradicts the assertion that all natural numbers > > > exist and are in lines of the list. > > > > Nope. > > > > Nope, two lines are necessary but not sufficient. > > Let's first prove that already two cannot be necessary by the fact > that two always can be replaced by one of them without changing the > contents. Then it is clear that two or more cannot be necessary and > from this immediately follows that they also cannot be sufficient.
Enough more than two line can be necessary and can be sufficient, outside of WMytheology. Inside WMytheology it is not apparent that anything can be either necessary or sufficient, since there cannot in WMytheology be all lines, or even infinitely many. > > > > Two lines can never do a better job than 1. > > > > Any finite number of lines is necessary but not sufficient. > > Wrong. Why do you resist to apply logic?
A positive finite number of lines in necessary unless no set of lines can be sufficient. But the set of all lines (at least outside WMytheology) is certainly sufficient. > > > > Any finite number of lines can never do a better job than 1. > > > > An infinite number of lines is necessary and sufficient > > Exercise: If of any two line one is not necessary, how many of > infinitely many lines are not necessary?
Infinitely many are not necessary provided infinitely many are still used.
For example, for any prime, the set of infinitely many lines ending in multiples of that prime are sufficient. Or even the set of lines ending in a prime. Or in the square o a prime, or the cube of a prime, and so on ad infinitum. > > > > An infinite number of lines can do a better job than 1 > > That is a confession of irrational belief. With exactly the same right > you could state: An infinite number of even naturals contains an odd > natural.
Only in WMytheology could an infinite number of even naturals contain an odd natural as life in WMytheology is totally unnatural.. > > You may claim so, but it is not part of mathematics.
No one outside of WMytheology is claiming so.
You should > accept: If someone claims infinity and is not even able to show two
A finite number of lines/FISs is not enough, at least outside of WMytheology because outside of WMytheology for any finite number of lines there is a natural in their union whose successor is not in their union. Wm claims tha this cannot happen in his WMytheology!
> > > > [In potential infinity things go > > > > Any number of findable lines is not sufficient > > > > An unfindable line is necessary and sufficient > > In any case the last line contains every number of the list.
That presumes a last line, but outside WMytheology in order to even be a line at all, a set of naturals has to have a successor set.
> This is > so by construction.
Then why is WM still so unable to construct the set of all binary sequences and the set of paths of a CIBT in the form of linear spaces and the obvious bijection between them as a linear mapping?
We have the choice between 1 line (in potential > infinity) and 0 lines (in actual infinity).