Point splitting technique in Pesking 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 $frac{g^{00}}{2} = frac{1}{2}$.