more from Herbert B. Enderton

Single Idea 13199

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set]

Full Idea

It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed.

Gist of Idea

The empty set may look pointless, but many sets can be constructed from it


Herbert B. Enderton (Elements of Set Theory [1977], 1:02)

Book Reference

Enderton,Herbert B.: 'Elements of Set Theory' [Posts + Telecoms 2006], p.2

A Reaction

This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction.