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Full Idea
We can form infinite ordinals by taking unions of ordinals. We can thus form 'limit ordinals', which have no immediate predecessor. ω is the first (the union of all finite ordinals), ω + ω = sω is second, 3ω the third....
Gist of Idea
The union of finite ordinals is the first 'limit ordinal'; 2ω is the second...
Source
Michal Walicki (Introduction to Mathematical Logic [2012], 2.3)
Book Ref
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.88
Related Idea
Idea 17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]