Do arity or dimension of relations depend on how many variables are involved? 1) y = x + 1 It seems like even though the above has both "=" and "+", there are only two variables, so the relation would be a binary one, where as... 2) z = x + y has 3 variables so there is a tertiary relation. Is this sensible or am I missing someone fundamental?

While $z=x+y$ is a boolean function of three variables, currying $y=1$ gets the two-variable function $z=x+1$. These facts identify such functions' minimal arities (the implementation of them might increase arity with unused arguments, e.g. `def f(x, y, z, a): return z==x+y` in Python has arity $4$).