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Effect of gravitation in set theory
Posted:
Nov 21, 2011 11:22 AM
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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
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