The question is, "Which of these relations on the set of all functions from $\mathbb{Z}$ to $\mathbb{Z}$ are equivalence relations.
$\{(f,g)|f(1)=g(1)\}$
I just want to make certain that I am interpreting this properly. So, $(f,g)$ is an element in the relation, right? But it can only be an element if $f$ and $g$, evaluated at one, are equal? And when the question says "of all functions," it means functions like $f(x)=x^2$? With this information, it can be reflexive, symmetric, and transitive, only if $f$ and $g$ are the exact same functions, is that correct?