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Single Idea 18099

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers ]

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 Ref

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]