Single Idea 8672

[catalogued under 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST]

Full Idea

The 'powerset' of a set is a set made up of all the subsets of a set. For example, the powerset of {3,7,9} is {null, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}}. Taking the powerset of an infinite set gets us from one infinite cardinality to the next.

Gist of Idea

A 'powerset' is all the subsets of a set

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.21


A Reaction

Note that the null (empty) set occurs once, but not in the combinations. I begin to have queasy sympathies with the constructivist view of mathematics at this point, since no one has the time, space or energy to 'take' an infinite powerset.