Full Idea
Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one.
Gist of Idea
Ordinals can define cardinals, as the smallest ordinal that maps the set
Source
report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.200