Single Idea 12337

[catalogued under 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST]

Full Idea

'Transitivity' signifies that all of the elements of the set are also parts of the set. If you have α∈Β, you also have α⊆Β. This correlation of membership and inclusion gives a stability which is the sets' natural being.

Gist of Idea

There is 'transivity' iff membership ∈ also means inclusion ⊆


Alain Badiou (Briefings on Existence [1998], 11)

Book Reference

Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.128

Related Ideas

Idea 13443 ∈ relates across layers, while ⊆ relates within layers [Hart,WD]

Idea 13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]

Idea 15500 Classes divide into subclasses in many ways, but into members in only one way [Lewis]

Idea 15499 A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis]