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).