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Topic: Effect of gravitation in set theory
Replies: 75   Last Post: Nov 25, 2011 7:11 PM

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 mueckenh@rz.fh-augsburg.de Posts: 12,659 Registered: 1/29/05
Effect of gravitation in set theory
Posted: Nov 21, 2011 11:22 AM

If we write all finite initial segments of the set |N in one line,
then we get |N:

1, 2, 3, ...

If we write all finite initial segments of the set |N below each
other, then we do not get |N:

1
1, 2
1, 2, 3
...

We only get every element of |N, but not in one single line, of
course.
At least two lines are necessary to contain them all. Or maybe an
infinity of lines? Unfortunately we cannot find a first line
necessary, although every set can be well-ordered, and the set of
lines is already well-ordered. So also every subset of lines is well-
ordered. Even the subset of lines that is necessary to contain all
elements of |N in their union. But this subset has no first line. What
a pity.

Regards, WM

Date Subject Author
11/21/11 mueckenh@rz.fh-augsburg.de
11/21/11 J. Antonio Perez M.
11/21/11 J. Antonio Perez M.
11/21/11 William Hughes
11/21/11 J. Antonio Perez M.
11/21/11 mueckenh@rz.fh-augsburg.de
11/21/11 Virgil
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 Virgil
11/22/11 Virgil
11/21/11 William Hughes
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 William Hughes
11/22/11 Virgil
11/22/11 J. Antonio Perez M.
11/21/11 Jürgen R.
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 Jürgen R.
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 Jürgen R.
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 J. Antonio Perez M.
11/22/11 Jürgen R.
11/22/11 J. Antonio Perez M.
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 Jürgen R.
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 Virgil
11/22/11 William Hughes
11/22/11 J. Antonio Perez M.
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 J. Antonio Perez M.
11/22/11 Virgil
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 William Hughes
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 J. Antonio Perez M.
11/22/11 William Hughes
11/22/11 Virgil
11/22/11 Virgil
11/22/11 Virgil
11/22/11 Virgil
11/22/11 Virgil
11/23/11 mueckenh@rz.fh-augsburg.de
11/23/11 Virgil
11/23/11 William Hughes
11/22/11 Virgil
11/22/11 J. Antonio Perez M.
11/22/11 Carsten Schultz
11/21/11 Virgil
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 William Hughes
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 William Hughes
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 William Hughes
11/22/11 mueckenh@rz.fh-augsburg.de
11/22/11 William Hughes
11/23/11 mueckenh@rz.fh-augsburg.de
11/23/11 William Hughes
11/23/11 Virgil
11/23/11 mueckenh@rz.fh-augsburg.de
11/23/11 Virgil
11/24/11 mueckenh@rz.fh-augsburg.de
11/24/11 Virgil
11/25/11 mueckenh@rz.fh-augsburg.de
11/25/11 J. Antonio Perez M.
11/25/11 mueckenh@rz.fh-augsburg.de
11/25/11 J. Antonio Perez M.
11/22/11 Virgil
11/22/11 Virgil
11/22/11 Virgil
11/22/11 Virgil
11/22/11 jdawe
11/22/11 J. Antonio Perez M.