In article <2bf7c594-8e66-4624-94d3-b1e05946811f@9g2000yqy.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 20 Feb., 23:27, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > For every natural number n we have > > > > the nth line of L and x > > > > are not coFIS > > > > > > true?- > > > > > True > > > > Is the statement > > > > There is no natural number m > > such that the mth line of L and x > > are coFIS > > > > true?- > > No, the statement is wrong. The true statement is: We cannot find the > largest number such that the mth line and x are coFIS. Again you > assume actual infinity for x. > > Consider the union of ordered sets in ZF: > (1, ) > (1, 2, ) > (1, 2, 3, )
While I am aware of sets in ZF standardly used to represent 1,2,3, and so on, and even 0, I am not aware of any set in ZF that represents a blank. And everything in ZF is a set, so without such a set there cannot be a blank in ZF. > > Each set has a blank.
Not in ZF. WM goofs as usual! > > Or consider the union of natural numbers in a set B while there > remains always one number in the intermediate reservoir A. > > A B > --> 1 -->{ } > --> 2,1 -->{ } > --> 2 -->1 > --> 3, 2 -->1 > --> 3 -->1, 2 > --> 4, 3 -->1, 2 > --> 4 -->1, 2, 3 > ... > --> n -->1, 2, 3, ..., n-1 > --> n+1, n -->1, 2, 3, ..., n-1 > --> n+1 -->1, 2, 3, ..., n-1, n > ... > > One would think that never all naturals can be collected in B, since a > number n can leave A not before n+1 has arrived. > > Of course this shows that ZF with its set of all natural numbers is > contradicted.
WM's A and B are not sets but sequences of sets, so if WM wants to consider a limit to any such sequences, he must first define what he means by such a limit, as there is no universal definition for "the" limit of a sequence of sets.
> Presumably it is this recognition that raises your > interest in potential infinity of analysis.
WM's presumptions are again wrong.
> Therefore the set > 0 > 10 > 110 > 1110 > ... > has a line that is coFIS with 111... (up to every n - and more is not > feasible).
Only in WMytheology.
Everywhere else a line containing 0 can never be coFIS with a line not containing 0. --
