They're not really dividing aleph_0 by aleph_1. The important thing is that it has measure 0, but you can easily have a set with cardinality aleph_1 and measure

They're not really dividing aleph_0 by aleph_1. The important thing is that it has measure 0, but you can easily have a set with cardinality aleph_1 and measure 0. There are also no ironic quotes around "equals". The measure really is 0.