Full Idea
An ordinal can be defined as a transitive set of transitive sets, or else, as a transitive set totally ordered by set inclusion.
Gist of Idea
Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion
Source
Michal Walicki (Introduction to Mathematical Logic [2012], 2.3)
Book Reference
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.89