Virgil
Posts:
8,833
Registered:
1/6/11


Re: (infinity) A real story
Posted:
Oct 13, 2013 6:11 PM


In article <3fe7c29b03ee44c29a2911e3b501751c@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Saturday, 12 October 2013 23:58:26 UTC+2, Virgil wrote: > > > > By construction of the sequence it is impossible that two or more finite > > > lines contain more than one of them. > > > Sufficiently more that 2 lines, namely infinitely many, will contain far > > more than any one line. > > If you claim that infinitely many enumerated lines are required, then name > the first line number required.
While no particular line is neccessary, neither is any finite set of lines sufficient, but any and every infinite set of lines is sufficient and the infiniteness of a set of lines is necessary.
> According to mathematics, every nonempty > subset of natural numbers has a first element. This also holds for infinite > subsets. Something true from WM. How outre! 

