quantum field theory - Point splitting technique in Peskin and Schroeder

One of the cornerstones of point splitting technique of calculating chiral anomaly (Peskin and Schroeder 19.1, p.655) is a symmetric limit $\epsilon \rightarrow 0$. And this is the point that I don't get. Is it really possible to take such a limit? For example, consider the expression $$ \text{symm}\,\text{lim}_{\epsilon \rightarrow 0} \Bigl\{\frac{\epsilon^{\mu}\epsilon^{\nu}}{\epsilon^2}\Bigr\} = \frac{g^{\mu \nu}}{d} \tag{19.23} $$ in $d=2$ spacetime dimensions. Let $\mu = \nu = 0$. Then $$ \frac{\epsilon^{0}\epsilon^{0}}{\epsilon^2} = \frac{1}{1-(\frac{\epsilon^1}{\epsilon^0})^2}. $$ But the latter expression either greater than 1 or less than 0 and so can't be equal to $$\frac{g^{00}}{2} = \frac{1}{2}.$$