On 17 Apr., 22:09, Virgil <vir...@ligriv.com> wrote: > In article > <7e4d8d16-1361-4e90-b2f3-8f75eeca2...@f18g2000vbs.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > Matheology 252 > > > The table T > > > 1 > > 2, 1 > > 3, 2, 1 > > ... > > n, ..., 3, 2, 1 > > ... > > > is a sequence of finite initial segments (1, ..., n) of natural > > numbers. It contains every natural number that can be somewhere. Every > > number in the sequence T is in one line L_n and in all further lines > > by construction of T (always the last line is added). > > If there is a last line, then what WM claims of T is false. > > Every number in > > > T is in the first column C (and in every other column too). > > > forall n : (1, ..., n) c C ==> (1, ..., n) e T > > forall n : (1, ..., n) e T ==> (1, ..., n) c C > > > Therefore it is impossible that C contains more than T and more than > > any line L_n of T. > > Only half true. A column contains no more that the whole table but > always contains more than any one row/line of that table.
Up to any line L_n it is clear that C contains not more than that line. If C should contain more than all lines, then it has to go beyond all lines. That is matheology.
C is a subset of the union of all lines. The union of all lines cannot contain more natural numbers than the sets of the sequence T of all lines, can it?
Do you really claim that when unioning the elements of T you get more natural numbers than are in the elements of T?
Then you have an opinion > from which all sane mathematicians are, thankfully, > forever banned by their sanity and logic.
Then you can act like a God and do abiogenesis: You union sets and get more elements than are in the sets. Of course you cannot name any one of the new elements. But you are sure, they have been created by you, Virgil, acting like a God.
And if you union again? Again create some creatures? Will this continue? Or is there some supremum?
My godness. What a perverted concept of the formerly so respected mathematics!