On 12 Mrz., 00:51, William Hughes <wpihug...@gmail.com> wrote: > On Mar 11, 10:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > You will never succeed in proving that pot. inf. is > > the same as act. inf, since your unsurmountable obstacle is the > > requirement that all natural numbers have to be in the list, but > > cannot be in one line but must be in one line. > > In the language of potential infinity, your famous > > all the natural numbers are in the first column > but not in any line becomes
You talk about the list
1 2, 1 3, 2, 1 ... ?
Here all columns contain all natural numbers, i.e., each one contains all.
> > There is a fixed column, C_1, which is coFIS to > |N. There is no fixed line which is coFIS to |N
There is no |N in potential infinity. > > There is no problem with either statment.
There is a problem with the statement, of actual infinity, that all natural numbers are in the list but not in any single line. This is in contradiction with the fact that 1) the union of two finite lines is always a subset of one of the two lines and 2) the list contains only finite lines.
This should somehow be removed in case of infinitely many lines, but it is not. Infinitely many finite numbers do not contain an infinite number. Infinitely many white balls do not contain a green cube.