Thread: Simple integer proof

1. Simple integer proof

I am currently taking my first proofs class, and I am finding it a little tougher than other math courses. This problem has me stuck for a proof, even though I find it obvious intuitively

Prop: If $m,n,p\in\mathbb{Z}$ such that $m+n=0$ and $m+p=0$ then $n=p$

2. Well you can say m+n=m+p and then add the additive inverse of m to both sides and continue

The Art of Proof has this exact proof outlined on the home page funny enough, it references another proposition so be sure to click the link in the proof

3. Well then you have $m+n=m+p$. Subtract $m$ from each side and you have it!

4. oh wow thanks a lot, I guess I didn't realize i could use that "transitive property of the equal sign" as it was never mentioned in class, but yeah that totally makes sense now

thanks again