WM zeigt daß 0=1!

15/05/2014 - 10:03 von karl | Report spam
Real Mathematik, nix für Conchita-Wurst-Matheologen!

Bin zu Faul, das zu übersetzen.

Assumption:

There are only countable many real numbers which can be enumerated in a list.
Easy to show that this is true using the binary from WM .

There is also only a countable number of real numbers in the unit interval which can be listed.
Let the numbers in this list denoted by (r_n)_{n \in IN}.

So now we take for each of these numbers r_n an interval containing I_n it as its center point with length:

l_n= d* 2^(-n)

where d is an arbitrary positive number. So:

I_n=[r_n - d* 2^(-n-1) , r_n + d* 2^(-n-1)]

So now the length of all these intervals must be larger than the length of the unit interval since there
are no other numbers in it than these countable set of numbers:

[0 , 1] \subset \cup_{n \in IN} I_n

For the length of the union of these set L we get an upper bound by summing the length l_n of all intervals I_n:

length([0, 1]) <= L <= \sum_{n=1}^{oo} l_n = \sum_{n=1}^{oo} d * 2^(-n) = 2 * d

Since d can be chosen as an arbitrary positive number, L can be made smaller than any positive number eps
wwe obtain that the length of the unit interval is less than any
positive number:

length([0, 1]) < eps

for all eps > 0.


From this we conclude, since the length of the unit interval is known to be unity, that:



0=1

Now, this can be done for all intervals of an arbitrary length a > 0 , we conclude therefore that:

0=a

So we have shown now that all positive real numbers are equal to zero if the assumption that there are only countable many
real numbers holds. The same then holds for negative numbers.

But since WM has shown without any doubt using the binary tree that the assumption is true, maths collapses into playing
around with zero.

Only zero exists!!
 

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#1 WM
21/05/2014 - 15:09 | Warnen spam
On Thursday, 15 May 2014 10:03:37 UTC+2, karl wrote:
Real Mathematik, nix für Conchita-Wurst-Matheologen!



Bin zu Faul, das zu übersetzen.



Assumption:



There are only countable many real numbers which can be enumerated in a list.

Easy to show that this is true using the binary from WM .


Only zero exists!!



Ja, die Annahme dass unendliche Mengen abgezàhlt, d.h., in Bijection gesetzt werden können, führt auf einen Widerspruch zur Mathematik. Das wird auf zwei Seiten hier bewiesen:
W. Mückenheim: "Das Paradoxon des Tristram Shandy", Forschungsbericht 2012, HS Augsburg, wmm wirtschaftsverlag, Augsburg (2012) p. 242-244.

http://www.hs-augsburg.de/medium/do...t_2012.pdf


Nach der Lektüre wird kaum jemand an der These festhalten wollen, dass ein Mensch, der tàglich 1000 EURO ausleiht und tàglich 1 EURO zurückzahlt, jemals schuldenfrei wird. Das ist bei genauer Betrachtung aber wesentlich leichter erreichbar als eine Abzàhlung aller Brüche, bei der der Eingang pro Rückzahlung von 1 nicht 1000 sonder unendlich viele rationale Zahlen betràgt.
http://www.hs-augsburg.de/~mueckenh/GU/GU12.PPT#461,64,Folie 64

Gruß, WM

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