  We construct some matroids that have a circuit and a cocircuit with infinite
intersection.
  This answers a question of Bruhn, Diestel, Kriesell, Pendavingh and Wollan.
It further shows that the axiom system for matroids proposed by Dress does not
axiomatize all infinite matroids. We show that one of the matroids we define is
a thin sums matroid whose dual isn't a thin sums matroid.
