  We present a new relation between an invariant of singularities in
characteristic zero (the log canonical threshold) and an invariant of
singularities defined via the Frobenius morphism in positive characteristic
(the F-pure threshold). We show that the set of limit points of sequences of
the form (c_p), where c_p is the F-pure threshold of an ideal on an
n-dimensional smooth variety in characteristic p, coincides with the set of log
canonical thresholds of ideals on n-dimensional smooth varieties in
characteristic zero. We prove this by combining results of Hara and Yoshida
with non-standard constructions.
