Cardinality of the set of all ordinals.

1. Feb 6, 2013

TylerH

What would the cardinality of the set of all ordinal numbers be? Is it even known or does the question even make sense in the case of such a weird, almost paradoxical set?

2. Feb 6, 2013

micromass

Staff Emeritus
The class of all ordinals doesn't form a set. There are simply too many ordinals to enclose them all in a set. Rather, the class of all ordinals forms a proper class. In ZFC set theory, there is no way to assign a cardinality to a proper class.

This should be interesting for you: http://en.wikipedia.org/wiki/Burali-Forti_paradox