The square of a transfinite cardinal number is the same number. The square of a transfinite ordinal number, however, is a (strictly) larger transfinite ordinal. For example, {omega_0}^2 = omega_0 * omega_0, where `*' represents ordinal multiplication. Both omega_0 and {omega_0}^2 have cardinality aleph_0, but they are distinct sets---omega_0 is a subset of {omega_0}^2, but the reverse is not true.