cardinal number CardinalNumber 2002-01-05 01:40:12 2007-01-23 10:55:48 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A cardinal number is an ordinal number $S$ with the property that $S \leq X$ for every ordinal number $X$ which has the same cardinality as $S$. Cardinal numbers have the property that for every set $A$, there exists a unique cardinal number having the same number of elements as $A$.