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
report of George Cantor (works [1880]) by Peter Koellner - On the Question of Absolute Undecidability 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.