Hypothesis testing, why alpha cannot be zero

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Alpha cannot be zero in hypothesis testing because it would lead to the automatic acceptance of the null hypothesis, rendering the testing process ineffective. Setting alpha to zero implies that only results with a probability of occurrence less than zero would be considered significant, which is impossible. This would eliminate the ability to detect any true effects or differences, undermining the purpose of hypothesis testing. Therefore, maintaining a non-zero alpha level is essential for meaningful statistical analysis. The discussion highlights the critical role of alpha in determining the significance of test results.
Deathfish
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Ok someone tell me the official explanation of why alpha cannot be zero in hypothesis testing.
 
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The UNOFFICIAL explanation (I don't know who could give you the "official" explanation) is that, if you set alpha to zero, you will always accept your null hypothesis, and thus hypothesis testing would be pointless.

Think about it. Testing at P < 0 means that you will call significant only a result that has probability less than 0 of happening if the null hypothesis is true. Obviously, there is never such a result.
 

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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