An infinite cardinal \(\kappa\) is called regular if it is not the union of less than \(\kappa\) smaller cardinals. Thus, \(\aleph_0\) is regular, and so are all infinite successor cardinals, such as \(\aleph_1\). Non-regular infinite cardinals are called singular. The first singular cardinal is \(\aleph_\omega\), as it is the union of countably-many smaller cardinals, namely \(\aleph_\omega =\bigcup_{n&lt;\omega} \aleph_n\).