Thank you for the clarification. Finally, a clear statement. What a relief!
But what does it have to do with the relativistic formula for addition of velocities, which is the topic of discussion now?
Oh, yes, regarding the fourth person,
As I said, they were
Him being a famous person was not important for my examples. To avoid this confusion, I strike him off the examples and replace with Ramin Machmudzade.
To summarize:
You have claimed,
and I gave you two counterexamples for each of these two claims:
for the first claim, Robert Phelan, Vlad Asinov,
for the second, Rosalie Arshak, Ramin Machmudzade.
The counterexamples refute the claims.
Here is this notion:
It can be an absolute unit of length in a homogeneous non-Euclidean space, but our physical space is non-homogeneous on smaller scales and might be Euclidean on larger scales, AFAIK.
Ignoring the references to "non-simultaneity", which I don't understand, my answer is:
In the frame S,
xA=0, tA=0, xB=10^6 km, tB=1 s.
If the frame S' moves with velocity 100000 km/s relative to S, then in S',
xA'=0, tA'=0, xB'=954594 km, tB'=-.118 s.
If I understand what you say, you are talking about two events, let's call them, event A and event B.
In the frame S, the coordinates of the events are respectively:
xA=0, tA=0 and xB=10^6 km, tB=1 s.
I still have no idea what the question, "What is velocity of non-simultaneity?" means.
Well, there is one more possibility, nCr(4,0) = 1.
If you count all the 'mixtures', then, instead of summation as you did above, you better calculate a simple total directly, which is 2n as @John Cuthber has explained earlier. And if you don't want to count the 'empty mixture' nCr(4,0), then the answer is simply 2n-1.
I want to clarify that I am not very comfortable with my own example of Turing Machine. Calling the instructions, a 'software' there is already a stretch. I think that it was von Neumann's idea to have instructions in memory like other data. This was the birth of software.
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