more from Herbert B. Enderton

Single Idea 13203

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets]

Full Idea

Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}.

Gist of Idea

The singleton is defined using the pairing axiom (as {x,x})


Herbert B. Enderton (Elements of Set Theory [1977], 2:19)

Book Reference

Enderton,Herbert B.: 'Elements of Set Theory' [Posts + Telecoms 2006], p.19

A Reaction

An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter!