On 21 Apr., 00:03, Virgil <vir...@ligriv.com> wrote: > In article > <ba068c96-ce1a-4a80-b84f-be765c029...@a14g2000vbm.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > There is no term s_n of S that contains all natural numbers. This > > condition requires > > (2) exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k. > > Nothing outside of Wolkenmuekenheim implies > "(2) exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k" > though it is implied often enough enough inside Wolkenmuekenheim.
Otherwise all naturals in s_k are in in s_j for k < j. This implies that all numbers in S are in one and the same s.
Consider the representation as a table
1 2, 1 3, 2, 1 ... n, ..., 2, 1 ...
All initial segments of |N (including |N itself) are in the first column, but not in the lines of the table? A provocation of mind. > > if (2) were true outside of > Wolkenmuekenheim, one would have both j < k and k < j simultaneously > true as well.