xRy in Z iff x,y > 0 Apparently this is the answer:
This is not an equivalence relation since 0 ∈ Z and 0 is not related to 0.
So I know that x relates to y iff x and y are in the same cell of the partition. What I am confused on is the notation x,y > 0. I understood that as both x and y are positive integers, but I don't understand the reasoning that "0 is not related to 0". Can someone please explain this to me please???
The notation $x, y > 0$ means "both $x$ and $y$ are greater than zero", so the definition of your relation $R$ is two integers are related if and only if they are both positive.
Now for it to be an equivalence relation $xRx$ must hold for all $x$. In particular, it must hold when $x = 0$. But we just said that $0R0$ holds if "both $0$ and $0$ are greater than zero". This is not true, so $0R0$ does not hold, so $R$ is not an equivalence relation.