  Extensive simulations are performed of the diffusion-limited reaction
A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction
rate profile, and the probability distributions of the separation and midpoint
of the nearest-neighbour pair of A and B particles, are all shown to exhibit
dynamic scaling, independently of the presence of fluctuations in the initial
state and of an exclusion principle in the model. The data is consistent with
all lengthscales behaving as $t^{1/4}$ as $t\to\infty$. Evidence of
multiscaling, found by other authors, is discussed in the light of these
findings.
