 In set theory a set is called transitive just in case all its elements are also subsets. An ordinal in the set-theoretic sense is a transitive set that is well-ordered by the elementhood relation \(\in\). It follows that each ordinal is the set of predecessors. According to the trichotomy above, there is a least ordinal (which is just the empty set) and all other ordinals are either successor or limit ordinals. The first limit ordinal is denoted by \(\omega\).