Full Idea
One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence.
Gist of Idea
We can understand cardinality without the idea of one-one correspondence
Source
Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3)
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.196
A Reaction
This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups.