WordNet (r) 3.0 (2006):

cardinality
    n 1: (mathematics) the number of elements in a set or group
         (considered as a property of that grouping)

The Free On-line Dictionary of Computing (30 December 2018):

cardinality

    The number of elements in a set.  If two sets
   have the same number of elements (i.e. there is a bijection
   between them) then they have the same cardinality.  A
   cardinality is thus an isomorphism class in the category
   of sets.

   aleph 0 is defined as the cardinality of the first
   infinite ordinal, omega (the number of natural
   numbers).

   (1995-03-29)