Das Kalenderblatt 091210

09/12/2009 - 13:08 von WM | Report spam
Cantor used the expression 2^aleph0 in order to represent the
magnitude of R set.
Since base 2 can be represented as a tree diagram, we can use it in
order to research a collection of infinitely many elements.
For example, let us look at the infinitely long Top_to_Bottom tree,
which is also represented as {1, 2, 4, 8, 16, ...}.
It is obvious that we always find finitely many leafs in any arbitrary
level of this tree, so this tree cannot have the magnitude of
2^aleph0.
Furthermore, since in any arbitrary level we are still in N set, we
can never define aleph0 as a transfinite number.
Now let us say that we start by a collection of infinitely many R
members, which are represented by infinitely many points.
In this case, we know that we can never start to use base 2 in order
to construct a Bottom_to_Top tree, if our collection of points can
construct a solid line, and if we do that, we discover that we get
infinitely many identical trees that cannot have |R| (if, again, R set
is like a solid line).
So my question is: How can we write 2^aleph0, if base 2 cannot exist
when we deal with |R|? [...]

Potential infinity (which never reaches Actual infinity, and therefore
cannot be completed) is the name of the game.

Also Cantor's proof, which is not based on the second diagonal method
is actually failed because of a very simple conceptual mistake, which
is:
If A set, c point, and B set are clearly distinguished from each
other, then there cannot be a gapless state between them, simple as
that!!

In short, Cantor uses simultaneously two different models
(3_distingueshed_states_AND_a_solid_line) that are clearly
contradicting each other.
Therefore this proof does not hold.
In short, the transfinite system does not exist.

[Doron Shadmi: "Transfinities" (2004)]
http://forum.wolframscience.com/sho...p;threadid`2

Gruß, WM
 

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#1 Carsten Schultz
09/12/2009 - 18:30 | Warnen spam
WM schrieb:
Cantor used the expression 2^aleph0 in order to represent the
magnitude of R set.
Since base 2 can be represented as a tree diagram, we can use it in
order to research a collection of infinitely many elements.


[...]
[Doron Shadmi: "Transfinities" (2004)]
http://forum.wolframscience.com/sho...p;threadid`2



Was Dein Kalenderblatt so lustig macht, ist, dass Du nicht zwischen
Mathematik, Philosophie und Unfug unterscheidest. Wie auch, schließlich
fehlen Dir die Kriterien dazu.

Gruß

Carsten

Carsten Schultz (2:38, 33:47)
http://carsten.codimi.de/
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