Hypothesis testing, why alpha cannot be zero

[Deathfish]

Ok someone tell me the official explanation of why alpha cannot be zero in hypothesis testing.

 

[pmsrw3]

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.