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Single Idea 10877

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI]

Full Idea

Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set.

Gist of Idea

Powers: All the subsets of a given set form their own new powerset


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

Book Reference

Clegg,Brian: 'Infinity' [Robinson 2003], p.206

A Reaction

Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set.