In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 7 Mai, 10:09, Virgil <vir...@ligriv.com> wrote: > > In article > > <4f39f1c3-6551-4e0d-9f20-02d1a9bf9...@g9g2000vbl.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 7 Mai, 00:14, Dan <dan.ms.ch...@gmail.com> wrote: > > > > > > 0.11111...... > > > > should also be a valid real number . > > > > Infinite digits ,corresponding to an infinite row, are as valid as > > > > infinite digits of the columns . > > > > > 0.11111...... it is not in the list > > > > > 0.1 > > > 0.11 > > > 0.111 > > > ... > > > > But, just like |N is the limit of the sequence of FISONs, > > it is the limit of your sequence. > > > The union of lines > cannot contain more elements than one line contains.
Unless there is some line that contains all other lines as subsets, it is inevitable that the union contain more than any one line.
Note that, at least outside of Wolkenmuekenheim, in any union of any family of sets, unless one of those sets already contains all the others as subsets, the union must always contain more than any single one of the sets being unioned. But according to WM that does not happen in Wolkenmuekenheim.
Thus the WM's religion, WMytheology, cannot apply anywhere outside of Wolkenmuekenheim.
On the other > hand, according to set theory, the union of all lines contains more > indices, namely |N, than than all lines. Contradiction.
Only more than in any line, which is quite different.
At least outside of WMytheology.
Theorem true everywhere except in Wolkenmuekenheim: Given a family of sets in which each set of the family is a proper subset of some other set of the family, then every set in the family is a proper subset of the union of that family. --