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Topic: Matheology § 062
Replies: 181   Last Post: Jul 14, 2012 1:48 PM

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Matheology § 062
Posted: Jul 7, 2012 5:06 AM
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Matheology § 062

Matheologians are accustomed to ignore the difference between
potential and actual infinity. Usually they even deny that there is
any difference. In this paragraph I will make another attempt to show
this difference.

Potential infinity is a never ending, never completed sequence or
chain of steps like the following, constructed of initial segments of
the ordered set of positive even numbers.

|{2}| = 1 < 2
|{2, 4}| = 2 < 4
|{2, 4, 6}| = 3 < 4, 6
|{2, 4, 6, 8}| = 4 < 6, 8
|{2, 4, 6, 8, 10}| = 5 < 6, 8, 10
|{2, 4, 6, 8, 10, 12}| = 6 < 8, 10, 12
...

This sequence is not more than all its terms. It cannot surpass all
its terms. It is incapable of reaching a cardinality larger than every
positive even number, the failure getting clearer and clearer with
every term at every step.

The existence of alephs, however, requires actual infinity, completed
infinity, finished infinity. But then we have to swallow results like
the following:

Consider an urn and infinitely many actions performed within one hour
(first one needs 1/2 hour, second one 1/4 hour, third one 1/8 hour and
so on).

Fill in 1, 2, remove 1
Fill in 3, 4, remove 2
Fill in 5, 6 remove 3
continue.

After 1 hour the urn is empty, because for every number the time of
removal can be determined. So for the set X of numbers residing in the
urn we obtain
Lim |X| =/= |Lim X|
This prevents any application of set theory to reality although it was
Cantor's outspoken aim to apply set theory to reality (cp., e.g., his
letter to Mittag-Leffler of Sept., 22, 1884).

Or assume the existence of all rational numbers of [0, 1], enumerated,
for instance, according to Cantor's method, starting with 0. If they
all exist, then all permutations should exist, because each number is
in finite distance from the first number 0, enumerated by 1. But then
also the permutation with all rational numbers enumerated and sorted
according to magnitude should be obtainable within aleph_0 steps and,
therefore, should exist, shouldn't it?

Therefore, in the latter cases, only potential infinity can prevail.
This is the true reason, why matheologians deny to recognize the
difference between potential and actual infinity. While most of the
followers certainly honestly claim that they never thought about that
problem, I cannot believe that the leading matheologians always have
observed the same ignorance.

Regards, WM



Date Subject Author
7/7/12
Read Matheology § 062
mueckenh@rz.fh-augsburg.de
7/7/12
Read Re: Matheology § 062
FredJeffries@gmail.com
7/7/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/8/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/8/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology § 062
William Hughes
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
William Hughes
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology § 062
William Hughes
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
William Hughes
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
Gus Gassmann
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
LudovicoVan
7/10/12
Read Re: Matheology § 062
William Hughes
7/10/12
Read Re: Matheology § 062
LudovicoVan
7/10/12
Read Re: Matheology § 062
William Hughes
7/10/12
Read Re: Matheology § 062
Jim Burns
7/10/12
Read Re: Matheology § 062
LudovicoVan
7/10/12
Read Re: Matheology § 062
Gus Gassmann
7/10/12
Read Re: Matheology § 062
LudovicoVan
7/10/12
Read Re: Matheology § 062
Gus Gassmann
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
Gus Gassmann
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
Gus Gassmann
7/11/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
Gus Gassmann
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology § 062
Gus Gassmann
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/11/12
Read Re: Matheology § 062
LudovicoVan
7/11/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
Gus Gassmann
7/12/12
Read Re: Matheology § 062
LudovicoVan
7/12/12
Read Re: Matheology § 062
William Hughes
7/12/12
Read Re: Matheology § 062
LudovicoVan
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
William Hughes
7/12/12
Read Re: Matheology § 062
Gus Gassmann
7/12/12
Read Re: Matheology § 062
LudovicoVan
7/12/12
Read Re: Matheology § 062
Gus Gassmann
7/12/12
Read Re: Matheology § 062
LudovicoVan
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
William Hughes
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
Gus Gassmann
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/12/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/12/12
Read Re: Matheology � 062
Virgil
7/13/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/13/12
Read Re: Matheology § 062
Marshall
7/13/12
Read Re: Matheology � 062
Virgil
7/13/12
Read Re: Matheology � 062
Virgil
7/13/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/13/12
Read Re: Matheology � 062
Virgil
7/13/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/13/12
Read Re: Matheology � 062
Virgil
7/13/12
Read Re: Matheology § 062
LudovicoVan
7/13/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
YBM
7/11/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/11/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
YBM
7/11/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/11/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
Gus Gassmann
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/10/12
Read Re: Matheology � 062
Virgil
7/12/12
Read Re: Matheology § 062
LudovicoVan
7/14/12
Read Re: Matheology § 062
LudovicoVan
7/14/12
Read Re: Matheology § 062
LudovicoVan
7/14/12
Read Re: Matheology § 062
William Hughes
7/14/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/10/12
Read Re: Matheology § 062
Ralf Bader
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
William Hughes
7/8/12
Read Re: Matheology § 062
William Hughes
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/8/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/9/12
Read Re: Matheology § 062
LudovicoVan
7/9/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology § 062
mueckenh@rz.fh-augsburg.de
7/8/12
Read Re: Matheology � 062
Virgil
7/7/12
Read Re: Matheology � 062
Virgil
7/8/12
Read Re: Matheology § 062
Graham Cooper
7/9/12
Read Re: Matheology § 062
Sam Gusset

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