Cardinality
Set theory
A measure of the size of a set. Two sets have the same cardinality when their elements can be matched one to one with none left over.
What is usually left out
For finite sets this reproduces counting. For infinite sets it produces genuinely different sizes: Cantor showed the reals cannot be matched one to one with the integers, so some infinities are strictly larger than others. The one-to-one criterion also makes a set the same size as some of its proper subsets, which is the defining oddity of the infinite.