MHB Summation and product notation rules

Thread starter lemonthree
Start date Oct 14, 2020
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Notation Product Rules Summation

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.

Oct 14, 2020

lemonthree

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?

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Oct 14, 2020

topsquark

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MHB

You are correct.

-Dan

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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