 Because we have this one-to-one correspondence between the cardinals and the ordinals, one might be tempted to say that the set of cardinals and the set of ordinals have the same order type, and then ask what the ordinal of this order type (and its cardinality) is. However, if there were such an ordinal, there would be a paradox—it would have to contain, and thus be larger than, all ordinals, including itself! This is the Burali-Forti paradox (see entry    paradoxes and contemporary logic). 