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Single Idea 18101

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number ]

Full Idea

If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes.

Gist of Idea

Each addition changes the ordinality but not the cardinality, prior to aleph-1

Source

David Bostock (Philosophy of Mathematics [2009], 4.5)

Book Ref

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.110

Related Idea

Idea 18106 Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock]