WM wrote: >>... consider the list of finite initial segments of natural numbers > 1 > 1, 2 > 1, 2, 3 > ... > > According to set theory it contains all aleph_0 natural numbers in its > lines. But is does not contain a line containing all natural numbers. > Therefore it must be claimed that more than one line is required to > contain all natural numbers. This means at least two line are > necessary.
That is correct. In fact, all Aleph_0 lines are required (necessary sufficient) to contain all of the naturals.