Im just curious... Why doesn´t this proof the Riemann Hypothesis? Where is it´s logical mistake:

When we assume - like Riemann did - that all the zeros are of the form c*i+[tex]\frac{1}{2}[/tex] we can say that this and only this has the property to give out zero when plugged into the Zeta Function.

We then can say that it must be true that c*i+[tex]\frac{1}{2}[/tex] \ne c*i+[tex]\frac{1}{r}[/tex] for every c \in R and for every c also every r \in R with r greater than 0, but smaller than 1 and r \ne 2.

This can easily be proofed by subtracting c*i from both sides like so:

c*i+[tex]\frac{1}{2}[/tex] \ne c*i+[tex]\frac{1}{r}[/tex] |-(c*i)

[tex]\frac{1}{2}[/tex] \ne [tex]\frac{1}{r}[/tex]

And this must be true, because as defined earlier r \ne 2