User blog comment:Googleaarex/Extended HyperNested Arrays/@comment-5029411-20130407182306/@comment-25418284-20130407213108

True, but it's also legal to define a cardinal \(C\) as the least ordinal with cardinality \(C\). That gives us \(\omega = \aleph_0\), \(\omega_1 = \aleph_1\), etc.