** Cardinals and Ordinals **

The cardinal number of a set is an indicator of the size of the set. It depends only on the elements of the set. Sets with the same cardinal number — or cardinality — are said to be equinumerate or (with unfortunate terminology) to be the same size. For finite sets there are no problems. Two sets, each having the same number of elements, both have cardinality . But an infinite set has the definitive property that it can be put in one-to-one correspondence with a proper subset of itself.