### Single Idea 17756

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

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 Reference

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]**