Continuum hypothesis
Set theory
The statement that no set has cardinality strictly between that of the natural numbers and that of the real numbers.
What is usually left out
It is a statement, not a question, and it is settled in a specific sense: Gödel (1940) showed it cannot be disproved from ZFC, and Cohen (1963) showed it cannot be proved from ZFC. It is therefore independent of the standard axioms, which is why it is not listed as open here in the way an unproved conjecture is.
Related terms
In the atlas
- generalized continuum hypothesis — Set theory, open