Can you prove or disprove (mn)!=m!n! for positive integers m and n?

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The statement (mn)! = m!n! for positive integers m and n is false, as demonstrated by the example (3*2)! = 720, which does not equal 3!2! = 12. The discussion also touches on proving that the square root of a prime integer is irrational, suggesting a proof by contradiction approach. The initial poster expresses confusion and seeks assistance with both mathematical claims. Additionally, a suggestion is made to post homework questions in a dedicated forum for better responses. The conversation highlights the importance of verifying mathematical identities and seeking help in appropriate channels.
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If m and n are positive integers, (mn)!=m!n! Prove or disprove.

its so obviously true i can't prove it. anyone help?

-also-

Prove: The square root of a prime integer is an irrational number.

any help?
 
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(3*2)! = 720 =/= 3!2! = 12

So it's actually FALSE.
 
hah wow, that shows how long i haven't slept.

any idea on the 2nd question?
 

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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