at t = 0, x = x', y = y' z = z' [ as per Galilean ]
or notated* as
x wrt (0,0,0)A = x' wrt(0,0,0)B
y wrt (0,0,0)A = y' wrt(0,0,0)B
z wrt (0,0,0)A = z' wrt(0,0,0)B
Given at t = 0, x wrt (0,0,0)A = 2, x' wrt (0,0,0)B = 2,
after letting vt = 3 [ vt to B, keeping A stationary ]
1) x wrt (0,0,0)A = 2
2) x' wrt (0,0,0)B = 2
3) x wrt (0,0,0)B = -1
4) x' wrt (0,0,0)A = +5
ALL 4 of these equations are mathematically true.
Indeed, I AM using notation that the Galilean does not.
*I challenge - Someone to use some other notation method, I do not care, so long as
that notations shows co-ordinates wrt to which system whenever THEY SAY x' = x-vt.
That is, which x' and which x in their two equations????
x' = x-vt
x = x'+vt
Anyone like to give this a try, please?
ADDED How about this notation?...( after vt ) cutting to the chase
xA = x'B
xB = xA -vt instead of x'B = xA -vt
x'A = x'B +vt instead of xA = x'B +vt
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."