more from Peter Koellner

### Single Idea 17889

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 4. The Infinite / g. Continuum Hypothesis]

Full Idea

Cantor's Continuum Hypothesis (CH) says that for every infinite set X of reals there is either a one-to-one correspondence between X and the natural numbers, or between X and the real numbers.

Gist of Idea

CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals

Source

Peter Koellner (On the Question of Absolute Undecidability [2006], 1.2)

Book Reference

-: 'Philosophia Mathematica' [-], p.7

A Reaction

Every single writer I read defines this differently, which drives me crazy, but is also helpfully illuminating. There is a moral there somewhere.