I'm already tr(r)

I shall begin by saying that I thought about this today in my Detection and Estimation Class while looking at the mse calculations for the MMSE estimator.
Let’s suppose we have a vector of discrete RVs player of elements playeri with the following rule:
i≠j⟹Pr{playeri=playerj}=0which means
i≠j⟹playeri≠playerjSuppose we are given a N×N square matrix R.
A square matrix has the operator Trace (tr) defined
as the sum of the elements on its main diagonal:
Suppose that the value tr(R) is part of the set of values that playeri can assume.
Now suppose that the variable playerA assumes the value of tr(R). Indeed:
playerA=tr(R)So playerA is Trace(R).
Let’s now suppose that also another random variable playerx, with x≠A wants to assume the role of Trace(R).
However,
Pr{playerx=tr(R)|playerA=tr(R)}=0Therefore, the variable playerx cannot assume the value of Trace(R) and should proceed to choose another value, since playerA is already Trace(R).
Sorry about this stupid meme.