Is there a notation for the last element in a set?

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In set theory, the last element of a set is not typically denoted since sets are unordered collections. The notation "max(p)" is used for the maximal element, but there is no widely recognized notation for the last element like "last(p)." The concept of a last element depends on the specific enumeration of the set rather than the set itself. In ordered contexts, such as paths in a graph, the last element can be identified, but this is not applicable to sets in general. Therefore, while there are ways to refer to the last element in ordered structures, it lacks formal recognition in standard set notation.
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Say set p = \left\{p_1, p_2,\ldots,p_n\right\}, how to notate p_n without saying p_n, since I'm not explicitly writing out p like that for a variety of reasons?
Like max(p) has the maximal element, what about last(p) or something? Is that recognized?
 
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If it is truly a set then no, that last element does not depend on the set, but on your enumeration of the set.
 
My p is a path on a graph from node 1 to 2 to 6, to etc, so here it's ordered in some sense or another...
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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