On 15 Mrz., 23:27, William Hughes <wpihug...@gmail.com> wrote: > On Mar 15, 8:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > Let's first prove that already two cannot be necessary by the fact > > that two always can be replaced by one of them without changing the > > contents. > > This is true but the fact that the two lines are > necessary has nothing to do with their contents. Two lines > cannot be replaced by one of them without changing the number > of lines.
Why should line-numbers be changed? Perhaps we are misunderstanding each other. This is my claim:
Here is a list with three lines containing five natural numbers
1) 1, 2, 3, 4 2) 1, 2, 3, 4, 5 3) 1, 2, 3, 4
We can remove lines 1 and 3 without reducing the contents ofthe list. Line number 2 remains line number 2.
> Consider the case is potential infinity. > A set of lines, K, that has an unfindable last number > must contain at least two findable lines. > The fact that these two lines are necessary has > nothing to do with the contents of the lines.
Here I would like to see an example.
But I would ask you in advance: Do you agree that every non-empty set of natural numbers (including line-numbers) has a smallest element? Or do you believe that here the exception proves the rule?