more from George Cantor

### Single Idea 18098

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST]

Full Idea

Cantor's diagonalisation argument generalises to show that any set has more subsets than it has members.

Gist of Idea

Cantor proved that all sets have more subsets than they have members

Source

report of George Cantor (works [1880]) by David Bostock - Philosophy of Mathematics 4.5

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.106

A Reaction

Thus three members will generate seven subsets. This means that 'there is no end to the series of cardinal numbers' (Bostock p.106).