MHB Easy question regarding symbols in discrete mathematics

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The set of symbols that constitute strings in discrete mathematics is denoted by the symbol Σ, representing the alphabet. In contrast, Σ* denotes the set of all finite strings that can be formed from the symbols in Σ, including the empty string. The Kleene Star (*) indicates that the strings can consist of zero or more symbols. Therefore, Σ refers to the basic set of symbols, while Σ* encompasses all possible combinations of those symbols. Understanding this distinction is fundamental in the study of formal languages and automata theory.
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is the set of symbols that make up strings denoted by the symbol Σ or Σ* , also what is this difference?
 
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Usually the set of symbols, or the alphabet, is denoted by $\Sigma$. Then $\Sigma^*$ denotes the set of all finite strings in the alphabet $\Sigma$.
 
The star (*) is the so called Kleene Star.
It means zero-or-more.

So indeed, Σ is the alphabet, while Σ* is the set of strings consisting of zero or more symbols from the alphabet.
 

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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