more from Brian Clegg

### Single Idea 10874

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification]

Full Idea

Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers.

Gist of Idea

Specification: a condition applied to a set will always produce a new set

Source

Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)

Book Reference

Clegg,Brian: 'Infinity' [Robinson 2003], p.205

A Reaction

What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers.