We show that two independent elephant random walks on the integer lattice $\mathbf{Z}$ meet each other finitely often or infinitely often depends on whether the memory parameter $p$ is strictly larger than $3/4$ or not. Asymptotic results for the distance between them are also obtained.

For any analytically finite Riemann surface, the Teichmüller modular group is countable, but it is not easy to find an analytically infinite Riemann surface for which the Teichmüller modular group is countable. In this paper, we determine whether the Teichmüller modular group is countable or uncountable for some analytically infinite Riemann surfaces defined by generalized Cantor sets.