Let G be a discrete subgroup of Iso(R2). Show that every subgroup of G is also discrete.
Isn't this true simply because it's a subgroup? So the elements of the subgroup are also in G?
We're talking about a subgroup of Iso (R2) so by discrete I have the definition:
G< Iso (R2) is discrete there exists an E such that
for all translation t_a in G, a < E
for all rotations in r_o in G, o<E
so the motions cannot be arbitrarily small. I understand what you mean, but I don't know how to apply it to this example.