MHB Verify Algebraic Statement for Philosophy of Time Essay

AI Thread Summary
The discussion revolves around verifying an algebraic statement for an essay on revising the A-series of time in light of relativity. The author seeks confirmation of the truth of the statement involving the sum of integers and their relationship to a variable y. A counterexample is provided, demonstrating that the assumptions about the integers can affect the validity of the conclusion. Strengthening the assumptions to strictly positive integers could lead to the desired conclusion. The author expresses gratitude for the assistance, indicating that this verification was crucial for completing the essay.
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I am not sure if this is the right thread, since I am new. Bump it if necessary.

I am currently writing an essay on revising the conventional A-series of time to account for relativity and simultaneity, among other problems. In the course of my argument, I have used an algebraic statement. I know that the organization is not up to convention, but this is a rough draft. I am just trying to verify that this is a true statement. I seem to remember some transitive property from my high school days that suggests that it is, but I want to make sure before my supervisor sees it! Thanks for the help!

Assuming
(1) all given variables represent non-zero integers and
(2) no integer in the addition operation appears more than once

-Let s represent the sum of following integers: m, n, x, p

If (s)(z) = y

then the following expressions must all be true:

(m)(z) ≠ y,
(n)(z) ≠y
(x)(z) ≠y.
(p)(z) ≠ y.



Mods: I was not sure where to post this since it is algebraic in nature but I am using it in a theoretical manuscript. Feel free to bump it wherever it belongs. Thanks for the help!
 
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Counterexample: $m=1, n=3, x=-2, p=-1$. Then $s=m+n+x+p=1$. We assume $sz=y$. But it is also true that $mz=y$. If you strengthen the first assumption to $m,n,x,p$ must all be strictly positive integers, then I think you could conclude what you want.
 
Thank you so much! Thanks to you, I have that essay under my belt; that was the last thing left to verify.

You have made Philosopher of Time very happy indeed. :D
 
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