> > The derivation is not straightforward at all. In fact it is hopelessly
> > flawed and makes me cringe.
> > Apart from the issue addressed by me in the quote, the initial equation
> > x=ut results for instance in dx/dt=u, whereas further down it reads
> > dx/dt=c and equivalently dx'/dt'=-u and dx'/dt'=c.
>
> That is because the equation
>         x = u t
> is the equation of motion of the origin of S' as seen in the
> S-frame, which therefore has velocity dx/dt = u according
> to the S-frame, whereas the equation of motion of the
> light signal according to the S-frame is
>         x = c t
> which of course has speed dx/dt = c according to the
> S-frame.

I know that, but this means that the variable x is defined twice here
1) it is the coordinate of the origin of S', 2) it is the coordinate of
the light signal, and taking the two equations above one gets u=c,
which is obviously nonsense.

>
> > On the other hand,
> > the conditions that x'=0 and x=0 for all times
>
> But these are not "conditions for all times".

Yes they are. According to the derivation, x'=0 is the location of the
origin of S' in S' (which obviously holds for all times). Equivalently
for x=0.

>
> > What a disaster of mathematical inconsistencies.
>
> Have you ever had analytical geometry in high school?
> What about the above don't you understand?

You should have noticed by now that analytical geometry can not be
applied here (that's the whole point about the invariance of the speed
of light).

Thomas