### 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 ⊆

Source

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]**