MHB Summation and product notation rules

AI Thread Summary
The discussion focuses on the validity of statements regarding summation and product notation rules. The user initially believes that only two statements are correct and identifies the third statement as incorrect, specifically regarding the distribution of a constant across a product. The conclusion confirms that the user's assessment is accurate, affirming that the third statement does not hold true. The conversation emphasizes the importance of understanding the properties of summation and product notation in mathematical expressions. Overall, the user successfully clarifies their understanding of the rules.
lemonthree
Messages
47
Reaction score
0
As per the image, I am supposed to select all the valid statements. Apparently I'm only partially correct, and so I took another look at the statements.

I believe the third statement is wrong, since $$c * (a_m*a_{m+1}*a_{m+2}*...*a_n)$$ =/= $$ (c*a_m)(c*a_{m+1})(c*a_{m+2})*...*(c*a_n)$$

Thus there should only be two answers. Am I correct on this?
 

Attachments

  • Capture.JPG
    Capture.JPG
    23.1 KB · Views: 119
Physics news on Phys.org
You are correct.

-Dan
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
Back
Top