continuum hypothesis
Cardinality gap question
The continuum hypothesis is a statement in set theory about the size of infinite sets: that there is no set whose cardinality falls strictly between that of the integers and the real numbers.
Put another way, the infinity of real numbers is the next-largest infinity after the countable infinity of whole numbers.
Proved by Gödel and Cohen to be independent of standard set theory—it can be neither proved nor disproved from the accepted axioms.
Size of a set
- CantorSet theory founder
- ordinalNumber denoting position
- real numbersComplete ordered field
- uncountableNot able to enumerate
Freedom from external control
- axiomsAccepted starting principles
- CohenPriestly lineage surname
- forcingCompelling through pressure
- consistencyReliable adherence to standards
Guess from limited facts
- open problemQuestion without known answer
- undecidableLacking possible proof
- independentFree from external control
- unresolvedLacking final determination
Hilbert's problems · question · inquiry · debate · speculation · pluralism
cardinality
Size of a set
- CantorSet theory founder
- ordinalNumber denoting position
- real numbersComplete ordered field
independence
Freedom from external control
consistency · incompleteness · foundations · formalism · determinacy
conjecture
Guess from limited facts
- open problemQuestion without known answer
- undecidableLacking possible proof
- independentFree from external control
unresolved · Hilbert's problems · question · inquiry · debate · speculation · pluralism
- Famous Problemstraveling salesman, Monty Hall, prisoner's dilemma, trolley problem, problem of evil
- Math Conjectures
- set theorysets, set, subset, superset, empty set
- mysteriesmystery, enigma, enigmas, puzzle, riddle
- logicpremise, premises, conclusion, conclusions, inference
- infinite combinatoricscolorings
continuous, continuity, hypothesis, continuum, hypothetical, hypothesize, discontinuous, hypothesized, hypothetically