# Need to verify a simple algebraic statement for an essay in the Philosophy of Time.

#### musickps

##### New member
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!

#### Ackbach

##### Indicium Physicus
Staff member
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.

#### musickps

##### New member
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.