On 24 Okt., 14:46, FredJeffries <fredjeffr...@gmail.com> wrote:
> You seem to be saying with your "infinite triangle" that you have an > ordered set of order type omega, the (ordered) set of lines. Each > element of this ordered set (lets call it A for reference) each > element of A is itself an ordered set. Since A is in fact well ordered > we may consider it indexed by the finite ordinals. The element at > index i (let's call it a_i) is a (finite) ordered set of order type i > (as an ordinal), so we may write a_i as (a_i_1, a_i_2, ..., a_i_i). > > Then you say something about the diagonal (a_1_1, a_2_2, a_3_3, ...) > having order type omega, but I don't understand what your point is.-
The limit of the set of lines has aleph_0 elements. But there is no line with infinitely many elements. The limit is not a maximum.
The diagonals (of the finite triangles) are identical to the lines. But it is said that the limit of the set of diagonals is taken. That is mysterious.