In article <7953bc45-4dfb-41df-b4cf-c4bb156876b2@n18g2000vbv.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 24 Okt., 10:57, SPQR <S...@roman.gov> wrote: > > > > I know your belief about the set of diagonals. My question is how you > > > can justify the difference to the set of lines. > > > > Each extension of a previous diagonal includes the prior elements in > > their prior positions, so there is no problem of whether a symbol in a > > new position is the same object as that symbol in a prior position, > > especially when that symbol in its prior position still exists. > > But isn't it independent of positions if a complet set is added to the > set of diagonals and a complet set is added to the set of lines?
But that does not happen! > > > > Can any object exist simulteneously in two positions at once? > > The representants (numerals) of objects (numbers) certainly can exist > in very different places simultaneously, for instance here 1 > and here 1.
Since it is the relative positions of those representatives that make your triangle, without them you have nothing. > > > > > > However it does not have a last element and it does not > > > > have an element d_oo. > > > > > "The diagonal" is the last element of the set of diagonals. > > > > Except that there is no such thing as a last element in the set of > > diagonals, or in the set of lines, in one of WM's "infinite triangle" > > structures.- > > I agree with your opinion. That is not very frequent. But I agree! > There is no last element in the set of diagonals. There is no omega > and no diagonal with omega elements, because that would be the first > transfinite one already, having no counterpart in the lines. But lines > and diagonal are identical during the whole process of construction.
If they were identical, there would be no way of distinguish between them, so your entire argument would go down the tubes.
