posted by Josh .
In discussing Frieze Groups it was assumed that there is a smallest positive translation along the axis. All translations for the pattern form a subgroup. Consider the axis to be the Reals and G to be a subgroup under +. Look at the infimum T of all strictly positive elements of G.
a) Show that if T is not the minimum of the strictly positive elements of G then T=0.Of course if T is minimum then T>0.