The crackpots' positions/arguments were put to sci.math
in such a way that at least two or three who posted re-
sponses thought it was your faq-er who was on the idiot's
side of the questions.

Their responses:

----------------------------------------------------------

I.   x0' = x0. In other words: x0' <> x0-vt, or "constant
     values on the x-axis are not subject to the transform".

AA: ====================================================================

  No.  x0' = x0 - vt.

  Well, if you want, you could define "constant values on the x-axis", but
in the context of the question that is not relevant.  The relevant fact is
that if the unprimed observer holds an object at point x0, then the
primed observer assigns to that object a coordinate x0' which is
numerically related to x0 by x0'= x0 -vt.

AA: ====================================================================
EE: ====================================================================

What does this mean? The line x=x0 will give x'=x-v*t=x0-vt', so if x0'
is to give the coordinate in the (x',t',)-system, it will be given by
x0'=x0-v*t': ie., it is not given by a constant. Thus, being at rest
(constant x-coordinate) is a coordinate-dependent concept.

EE: ====================================================================
GG: ====================================================================

Sounds very false. We can say that the representation of the point X0 is
the number x0 in the unprimed system, and x0' in the primed system.
Clearly x0 and x0' are different, if vt is not zero. However one may say
that (though it sounds/is stupid) the point X0 itself "is the same
throughout the transformation". However that expression sounds
meaningless, since a transform (ok, maybe we should call it a change of
basis) is only a function that takes the point's representation in one
system into the same point's representation in another system. It is
preferrable to use three notations: X0 for the point itself and x0 and
x0' for the points' representations in some coordinate systems.

GG: ====================================================================