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I've always used the Lorentz dilation/contraction approach and
realized early on that it is the impossibility of simultaneity that
is often overlooked.
There's no nice 'equation' to sum it up as there
is for time and space intervals.
Two events that are simultaneous in one frame CANNOT be simultaneous
in ANY OTHER frame.
(unless of course they are at the same location as well as the same
time -
in which case I'll claim that they are only ONE event - not two.)