Date: Apr 17, 2013 8:18 AM
Subject: Matheology §252

Matheology §252

The table T

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). 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. But we know that there is no line L_n with an
actually infite set |N of numbers (because T is a sequence of finite
lines L_n). Conclusion: An actually infinite set |N cannot be in the
first column either (and nowhere else).

Regards, WM