 Next the notion of greater than arbitrary cardinals, finite and infinite. The cardinal number of \( \alpha \) is greater than the cardinal number of \( \beta \) just in case there is a subset of \( \alpha \) that is equinumerous with \( \beta \), but there is no subset of \(\beta \) that is equinumerous with \(\alpha \). Cantor’s famous “diagonal argument” shows that cardinal number \( \aleph_c \) of the class of real numbers is greater than \( \aleph_0 \), the cardinal number of the class of natural numbers. 