 \(x_0,x_1,x_2, \dots\) are used as formal variables over \(\mathbb{N}\) for the purpose of indicating the argument of functions. \(x,y,z,\ldots\) will also be used informally for arbitrary variables from this list. \(\vec{x}\) will be used to abbreviate a vector of variables \(x_0,\ldots,x_{k-1}\) (when the arity is clear from context).