Full Idea
It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers.
Gist of Idea
The number of reals is the number of subsets of the natural numbers
Source
David Bostock (Philosophy of Mathematics [2009], 4.5)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.107
A Reaction
The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers?
Related Idea
Idea 18098 Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]