Date: Apr 17, 2013 8:18 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology §252
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). 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