Small and large earthquakes obey different scaling laws and inhabit di
stinct populations, both characterized by power laws with different, e
xponents, When considering earthquakes on a single fault or fault segm
ent, the one large earthquake that occurs during a seismic cycle is di
scontinuous with the population of small earthquakes. Here it is shown
that these two observations, together with the scaring laws, are self
-consistent when groper account is taken of the size distribution of f
aults.