On 22 Apr., 21:18, Virgil <vir...@ligriv.com> wrote: > In article > <a0dc77ed-6546-41c9-8d89-8315c71b3...@c9g2000vbr.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 21 Apr., 22:02, Virgil <vir...@ligriv.com> wrote: > > > > > Consider the representation as a table > > > > > 1 > > > > 2, 1 > > > > 3, 2, 1 > > > > ... > > > > n, ..., 2, 1 > > > > ... > > > > > All initial segments of |N (including |N itself) are in the first > > > > column, but not in the lines of the table? > > > Can you name an n that is in a column but not in a horizontal line? > > For any given horizontal line, I can.
The question is for all horizontal lines. > > > If not, why do you believe that the comlums contain more than every > > horzontal line? > > Why do you misrepresent what I said so obviously? > > Given any column and any line, > that column contains numbers not in that line.
That is not the question. The question is whether there is a line with all nunbers of the columns. > > But the union of the set of all columns and the union of the set of all > lines are the same.
The union of the set of all lines is a line, since every line is the union of all preceding lines. Therefore, if we have infinitely many lines, we have infinitely many unions. More is not possible, is it?
> > > And you have not shown how it is possible to have more naturals in a > > column than in every horizontal line. Nevertheless you claim to have > > shown that erroneously. > > No! You claim erroneously that I have claimed it. > But it is your quantifier dyslexia at work again.
Drop your edrroneous understanding of quantifiers. Answer the mathematical questions: 1) Is there a line with infinitely many numbers? 2) Is there a number in the first column that is not in a line together with all its preceding numbers?
> > What I actually claimed is that there are more naturals in ANY ONE > column than in ANY ONE line, but did NOT claim more naturals in all > columns collectively than in all lines collectively.
All that is contained in all lines collectively, is also contained in one single line s_i. Or exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.