On 20 Mrz., 14:00, William Hughes <wpihug...@gmail.com> wrote: > On Mar 20, 1:17 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > > > So your proof that any two lines can be replaced > > > by one line without changing the contents is irrelevant. > > > Since contents can only exist in lines, and since every line is > > superset to all its predecessors, the proof is correct. > > The proof is irrelevant (it is, however, correct)
Nice to hear. Not that I had any doubt, but it is nice to hear that you have no doubt too.
> since showing that lines are not needed for their > contents does not show that the lines are not needed.
The lines were invented by myself solely for this purpose.
The first question is: Is the first line necessary to have the number 1 in the list.
Formulated somewhat more "mathematically": Is the union of all lines different from the union of all lines except the first one.
Then go to the second question.
> To show that actual infinity is unreasonable you > have to show the lines are not needed.
I show that every line, that is not the last line, is not needed. Since there is not a last line in actual infinity, this shows that all lines are not needed.
The unreasonable argument is this: "There are all lines, but there is no last line." It has been pasted together from: Every natural number can be regonized as such. For every natural number there is a next one.