On Saturday, June 15, 2013 1:35:21 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Friday, 14 June 2013 21:11:16 UTC+2, Zeit Geist wrote: > > > The symmetry does prevIail. The three Unions in the "completed" list all have same number of elements. > > > 1 > > 11 > > 111 > > ... > > > > The hight and diagonal have aleph_0 elements. Is there a line with aleph_0 elements? >
For all n e N, the n-th line contains n 1's.
The diagonal is the sequence of the n-th element of the n-th line, for all n e N. The first column is the sequence of the 1-th element of the n-th line, for all n e N.
For all n e N, the diagonal is not completed at the n-th line. For all n e N, the first column is not completed at the n-th line. For all n e N, the line with aleph_0 1's is not completed at the n-th line.
Previous post show all these objects are identical.
The Axiom of Infinity allows us to show these objects exist.
You may choose to reject AoI, but accepting it does not lead to a contradiction.